DSA211_Project
2023-02-16
Scenario
Based on 2022 Singapore HDB resale price (real-life) data sets, your team is supposed to construct a multiple regression model (for one particular district) to explain the HDB resale price (ResalePrice) in dollars with the given independent variables.
- Date: Transaction Month
- Type: HDB Types (3-, 4- or 5-room flats)
- Block: Block Number of Flat
- Street: Flat’s Street Location
- Story: Flat’s Story
- Area: Size in Squared Meters
- Model: Flat’s Model
- LeaseBegin: Year of Lease Start
- LeaseRemain: Period of Lease Remaining
Marking Criteria
Documentation and Presentation: 10 marks
Methodology: 10 marks
R-codes, computer outputs interpretation and graphical explanations: 15 marks
Recommendations and conclusions: 15 marks
Format:
Written Report: PDF Format: Within 10pages excluding the cover page and Appendix
Appendix: codes with computer outputs
You are required to provide the detailed documentation of how you search your recommended model for inference purpose and justify each step in your data analysis. You are also expected to provide model assumption justification and hypothesis testing evidences (R-codes and computer outputs) with clear explanations that your recommended model is the best model among all the models considered according to BIC criterion. Based on your final recommended model, state clearly your recommendations and conclusions.
Part 1 of Project
Load Data In
Sengkang1 <- read.csv("data/Sengkang2023P.csv", stringsAsFactors = TRUE)
head(Sengkang1, 5)## Date Type Block Street Story Area Model LeaseBegin LeaseRemain
## 1 2022-01 3 ROOM 331C ANCHORVALE ST 10 TO 12 67 Model A 2015 92 years 09 months
## 2 2022-01 3 ROOM 209C COMPASSVALE LANE 16 TO 18 67 Model A 2011 88 years 11 months
## 3 2022-01 3 ROOM 211C COMPASSVALE LANE 10 TO 12 68 Model A 2013 90 years 02 months
## 4 2022-01 3 ROOM 467B FERNVALE LINK 04 TO 06 68 Model A 2016 93 years 08 months
## 5 2022-01 3 ROOM 414B FERNVALE LINK 07 TO 09 68 Model A 2016 93 years 01 month
## ResalePrice
## 1 420000
## 2 418000
## 3 410000
## 4 382000
## 5 410000For visualisation purposes and model creation ideas
library(httr)
geocode <- function(block, streetname) {
base_url <- "https://developers.onemap.sg/commonapi/search"
address <- paste(block, streetname, sep = " ")
query <- list("searchVal" = address,
"returnGeom" = "Y",
"getAddrDetails" = "N",
"pageNum" = "1")
res <- GET(base_url, query = query)
restext<-content(res, as="text")
output <- jsonlite::fromJSON(restext) %>%
as.data.frame() %>%
dplyr::select("results.LATITUDE", "results.LONGITUDE")
return(output)
}Sengkang$LATITUDE <- 0
Sengkang$LONGITUDE <- 0
for (i in 1:nrow(Sengkang)){
temp_output <- geocode(Sengkang[i, 3], Sengkang[i, 4])
Sengkang$LATITUDE[i] <- temp_output$results.LATITUDE
Sengkang$LONGITUDE[i] <- temp_output$results.LONGITUDE
}write_rds(Sengkang, file ="Sengkang_coords")Sengkang <- read_rds("Sengkang_coords")Sengkang_sf <- st_as_sf(Sengkang, coords = c("LONGITUDE", "LATITUDE"), crs = 4326) |>
st_transform(crs = 3414)
glimpse(Sengkang_sf)## Rows: 2,116
## Columns: 11
## $ Date <chr> "2022-01", "2022-01", "2022-01", "2022-01", "2022-01", "2022-01", "2022-01", "…
## $ Type <chr> "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM"…
## $ Block <chr> "331C", "209C", "211C", "467B", "414B", "467A", "414B", "414B", "453A", "472B"…
## $ Street <chr> "ANCHORVALE ST", "COMPASSVALE LANE", "COMPASSVALE LANE", "FERNVALE LINK", "FER…
## $ Story <chr> "10 TO 12", "16 TO 18", "10 TO 12", "04 TO 06", "07 TO 09", "19 TO 21", "16 TO…
## $ Area <int> 67, 67, 68, 68, 68, 68, 68, 68, 67, 68, 67, 67, 68, 67, 67, 68, 68, 68, 67, 68…
## $ Model <chr> "Model A", "Model A", "Model A", "Model A", "Model A", "Model A", "Model A", "…
## $ LeaseBegin <int> 2015, 2011, 2013, 2016, 2016, 2016, 2016, 2016, 2015, 2016, 2015, 2015, 2017, …
## $ LeaseRemain <chr> "92 years 09 months", "88 years 11 months", "90 years 02 months", "93 years 08…
## $ ResalePrice <int> 420000, 418000, 410000, 382000, 410000, 408000, 412000, 400000, 405000, 350000…
## $ geometry <POINT [m]> POINT (34282.7 41941.51), POINT (35328.82 40660.61), POINT (35341.91 407…library(tmap)
sengkang_sp <- Sengkang_sf %>%
mutate(subzone = as.factor(ifelse(grepl("^1", Block), "Rivervale",
ifelse(grepl("^2", Block), "Compassvale",
ifelse(grepl("^3", Block), "Anchorvale",
ifelse(grepl("4", Block), "Fernvale", "others"))))),
Date = lubridate::ym(Date),
LeaseBegin = lubridate::ym( paste0(LeaseBegin,"-01")),
years_used = as.numeric((Date - LeaseBegin)/365)) %>%
as_Spatial()
tmap_mode("view")## tmap mode set to interactive viewingtm_shape(sengkang_sp) +
tm_dots(col = "subzone")Initial regression with original dataset
L0 <- lm(ResalePrice ~.,
data = Sengkang1)
summary(L0)##
## Call:
## lm(formula = ResalePrice ~ ., data = Sengkang1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -104398 -10412 0 10782 74298
##
## Coefficients: (38 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 135214.5 71692.3 1.886 0.059503 .
## Date2022-02 -471.3 3390.7 -0.139 0.889468
## Date2022-03 -2206.6 4379.5 -0.504 0.614449
## Date2022-04 2319.3 5457.1 0.425 0.670892
## Date2022-05 -604.7 6502.8 -0.093 0.925921
## Date2022-06 1159.1 7731.2 0.150 0.880843
## Date2022-07 1113.0 8904.3 0.125 0.900542
## Date2022-08 852.0 10162.7 0.084 0.933198
## Date2022-09 6211.8 11555.1 0.538 0.590958
## Date2022-10 3538.0 12893.7 0.274 0.783819
## Date2022-11 7377.6 14140.1 0.522 0.601931
## Date2022-12 6234.2 15435.3 0.404 0.686355
## Type4 ROOM 52840.0 19613.6 2.694 0.007146 **
## Type5 ROOM 127382.5 34636.9 3.678 0.000245 ***
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## StreetANCHORVALE DR NA NA NA NA
## StreetANCHORVALE LANE NA NA NA NA
## StreetANCHORVALE LINK NA NA NA NA
## StreetANCHORVALE RD NA NA NA NA
## StreetANCHORVALE ST NA NA NA NA
## StreetCOMPASSVALE BOW NA NA NA NA
## StreetCOMPASSVALE CRES NA NA NA NA
## StreetCOMPASSVALE DR NA NA NA NA
## StreetCOMPASSVALE LANE NA NA NA NA
## StreetCOMPASSVALE LINK NA NA NA NA
## StreetCOMPASSVALE RD NA NA NA NA
## StreetCOMPASSVALE ST NA NA NA NA
## StreetCOMPASSVALE WALK NA NA NA NA
## StreetFERNVALE LANE NA NA NA NA
## StreetFERNVALE LINK NA NA NA NA
## StreetFERNVALE RD NA NA NA NA
## StreetFERNVALE ST NA NA NA NA
## StreetJLN KAYU NA NA NA NA
## StreetRIVERVALE CRES NA NA NA NA
## StreetRIVERVALE DR NA NA NA NA
## StreetRIVERVALE ST NA NA NA NA
## StreetRIVERVALE WALK NA NA NA NA
## StreetSENGKANG CTRL NA NA NA NA
## StreetSENGKANG EAST AVE NA NA NA NA
## StreetSENGKANG EAST RD NA NA NA NA
## StreetSENGKANG EAST WAY NA NA NA NA
## StreetSENGKANG WEST AVE NA NA NA NA
## StreetSENGKANG WEST WAY NA NA NA NA
## Story04 TO 06 25826.9 2241.4 11.522 < 2e-16 ***
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## Story10 TO 12 50795.2 2290.4 22.178 < 2e-16 ***
## Story13 TO 15 58879.1 2212.6 26.610 < 2e-16 ***
## Story16 TO 18 72417.6 2813.3 25.742 < 2e-16 ***
## Story19 TO 21 67083.9 4054.2 16.547 < 2e-16 ***
## Story22 TO 24 76787.4 4611.7 16.651 < 2e-16 ***
## Story25 TO 27 73484.8 6188.6 11.874 < 2e-16 ***
## Area 2383.5 764.7 3.117 0.001867 **
## ModelModel A 14764.4 3244.0 4.551 5.81e-06 ***
## ModelModel A2 NA NA NA NA
## ModelPremium Apartment NA NA NA NA
## LeaseBegin NA NA NA NA
## LeaseRemain75 years 03 months 13185.3 32710.8 0.403 0.686948
## LeaseRemain75 years 04 months -25239.7 40074.0 -0.630 0.528913
## LeaseRemain75 years 05 months 35728.2 37333.5 0.957 0.338737
## LeaseRemain75 years 06 months 8163.5 39280.8 0.208 0.835398
## LeaseRemain75 years 07 months 4803.0 38561.0 0.125 0.900893
## LeaseRemain75 years 08 months 554.5 37786.9 0.015 0.988295
## LeaseRemain75 years 09 months -8471.4 38833.7 -0.218 0.827349
## LeaseRemain75 years 10 months -13030.3 38303.4 -0.340 0.733769
## LeaseRemain75 years 11 months -41236.9 38680.5 -1.066 0.286573
## LeaseRemain76 years -1313.4 40936.1 -0.032 0.974409
## LeaseRemain76 years 01 month -7069.7 40325.3 -0.175 0.860856
## LeaseRemain76 years 02 months -5701.6 41595.3 -0.137 0.890994
## LeaseRemain76 years 03 months -32214.5 42057.5 -0.766 0.443831
## LeaseRemain76 years 04 months -46821.6 43524.0 -1.076 0.282224
## LeaseRemain76 years 05 months -53271.9 43687.1 -1.219 0.222906
## LeaseRemain76 years 06 months -55370.2 44176.0 -1.253 0.210277
## LeaseRemain76 years 07 months -55774.5 45750.8 -1.219 0.223022
## LeaseRemain76 years 08 months -70629.9 46236.6 -1.528 0.126851
## LeaseRemain76 years 09 months -80201.3 47090.5 -1.703 0.088773 .
## LeaseRemain76 years 10 months -82596.6 48578.9 -1.700 0.089312 .
## LeaseRemain76 years 11 months -83540.1 49530.0 -1.687 0.091900 .
## LeaseRemain77 years -76948.6 51146.8 -1.504 0.132694
## LeaseRemain77 years 01 month -80159.5 51520.4 -1.556 0.119971
## LeaseRemain77 years 02 months -99233.6 52575.0 -1.887 0.059311 .
## LeaseRemain77 years 03 months -88741.5 53288.6 -1.665 0.096085 .
## LeaseRemain77 years 04 months -90678.2 54037.4 -1.678 0.093565 .
## LeaseRemain77 years 05 months -108147.0 55527.6 -1.948 0.051666 .
## LeaseRemain77 years 06 months -120952.2 56272.7 -2.149 0.031780 *
## LeaseRemain77 years 07 months -114989.4 57187.2 -2.011 0.044549 *
## LeaseRemain77 years 08 months -113515.0 58501.2 -1.940 0.052540 .
## LeaseRemain77 years 09 months -134690.7 59837.5 -2.251 0.024549 *
## LeaseRemain77 years 10 months -137906.4 60881.9 -2.265 0.023661 *
## LeaseRemain77 years 11 months -148388.5 62010.8 -2.393 0.016849 *
## LeaseRemain78 years -132337.9 63276.0 -2.091 0.036675 *
## LeaseRemain78 years 01 month -139203.8 64098.0 -2.172 0.030049 *
## LeaseRemain78 years 02 months -145582.0 65163.1 -2.234 0.025638 *
## LeaseRemain78 years 03 months -154977.0 66297.5 -2.338 0.019553 *
## LeaseRemain78 years 04 months -159300.1 67525.9 -2.359 0.018461 *
## LeaseRemain78 years 05 months -172362.4 68814.1 -2.505 0.012370 *
## LeaseRemain78 years 06 months -172829.7 71031.9 -2.433 0.015098 *
## LeaseRemain78 years 07 months -157083.7 71250.4 -2.205 0.027645 *
## LeaseRemain78 years 08 months -171340.4 72262.5 -2.371 0.017875 *
## LeaseRemain78 years 09 months -179444.1 74024.9 -2.424 0.015476 *
## LeaseRemain78 years 10 months -188942.2 75376.6 -2.507 0.012305 *
## LeaseRemain78 years 11 months -171133.5 76427.8 -2.239 0.025308 *
## LeaseRemain79 years -191657.9 77618.1 -2.469 0.013663 *
## LeaseRemain79 years 01 month -183450.8 79581.0 -2.305 0.021305 *
## LeaseRemain79 years 02 months -209419.8 80178.3 -2.612 0.009103 **
## LeaseRemain79 years 03 months -188180.0 82655.3 -2.277 0.022961 *
## LeaseRemain79 years 04 months -176720.3 83551.2 -2.115 0.034603 *
## LeaseRemain79 years 05 months -216351.3 84472.6 -2.561 0.010539 *
## LeaseRemain79 years 06 months -223733.3 85586.7 -2.614 0.009045 **
## LeaseRemain79 years 07 months -236027.8 87027.6 -2.712 0.006770 **
## LeaseRemain79 years 08 months -228235.0 87620.0 -2.605 0.009293 **
## LeaseRemain79 years 09 months -235583.6 89625.0 -2.629 0.008672 **
## LeaseRemain79 years 10 months -237592.8 90591.8 -2.623 0.008822 **
## LeaseRemain79 years 11 months -227788.2 92153.1 -2.472 0.013564 *
## LeaseRemain80 years -222994.3 93143.3 -2.394 0.016797 *
## LeaseRemain80 years 01 month -246676.5 94422.0 -2.612 0.009088 **
## LeaseRemain80 years 02 months -240987.5 95430.7 -2.525 0.011675 *
## LeaseRemain80 years 03 months -272119.3 97303.8 -2.797 0.005237 **
## LeaseRemain80 years 04 months -269702.3 98621.6 -2.735 0.006325 **
## LeaseRemain80 years 05 months -268617.6 99667.5 -2.695 0.007123 **
## LeaseRemain80 years 06 months -248951.0 101720.2 -2.447 0.014515 *
## LeaseRemain80 years 07 months -300030.1 103616.8 -2.896 0.003845 **
## LeaseRemain80 years 08 months -276533.5 103628.8 -2.669 0.007710 **
## LeaseRemain80 years 09 months -202986.7 110084.2 -1.844 0.065413 .
## LeaseRemain80 years 10 months -293615.6 106083.4 -2.768 0.005721 **
## LeaseRemain80 years 11 months -279974.6 108360.4 -2.584 0.009878 **
## LeaseRemain81 years -264229.4 110387.0 -2.394 0.016816 *
## LeaseRemain81 years 01 month -284504.8 111323.2 -2.556 0.010707 *
## LeaseRemain81 years 02 months -288020.2 113818.1 -2.531 0.011502 *
## LeaseRemain81 years 03 months -294508.1 114351.5 -2.575 0.010116 *
## LeaseRemain81 years 04 months -298456.9 114926.7 -2.597 0.009508 **
## LeaseRemain81 years 05 months -279721.5 117288.6 -2.385 0.017221 *
## LeaseRemain81 years 06 months -332002.0 118577.4 -2.800 0.005185 **
## LeaseRemain81 years 07 months -334194.0 120502.9 -2.773 0.005625 **
## LeaseRemain81 years 08 months -307547.4 121188.1 -2.538 0.011267 *
## LeaseRemain81 years 09 months -353040.0 123357.3 -2.862 0.004275 **
## LeaseRemain81 years 10 months -359052.4 123940.3 -2.897 0.003828 **
## LeaseRemain81 years 11 months -324702.8 125523.8 -2.587 0.009791 **
## LeaseRemain82 years -355135.3 127080.3 -2.795 0.005270 **
## LeaseRemain82 years 01 month -345273.5 128163.6 -2.694 0.007147 **
## LeaseRemain82 years 02 months -345291.3 130372.3 -2.649 0.008179 **
## LeaseRemain82 years 03 months -383366.0 131891.5 -2.907 0.003712 **
## LeaseRemain82 years 04 months -425762.8 134359.0 -3.169 0.001565 **
## LeaseRemain82 years 05 months -409517.6 134869.7 -3.036 0.002440 **
## LeaseRemain82 years 06 months -404799.4 137287.9 -2.949 0.003247 **
## LeaseRemain82 years 07 months -394375.3 137253.3 -2.873 0.004125 **
## LeaseRemain82 years 08 months -399714.4 138230.4 -2.892 0.003893 **
## LeaseRemain82 years 09 months -419698.9 139508.4 -3.008 0.002675 **
## LeaseRemain82 years 10 months -417229.7 140788.8 -2.964 0.003095 **
## LeaseRemain82 years 11 months -449938.9 142191.5 -3.164 0.001589 **
## LeaseRemain83 years -451998.9 143709.4 -3.145 0.001696 **
## LeaseRemain83 years 01 month -451163.6 147677.2 -3.055 0.002294 **
## LeaseRemain83 years 02 months -427662.3 146771.7 -2.914 0.003629 **
## LeaseRemain83 years 10 months 105956.7 49973.4 2.120 0.034166 *
## LeaseRemain83 years 11 months 141006.6 52923.1 2.664 0.007805 **
## LeaseRemain84 years 53570.9 45539.9 1.176 0.239661
## LeaseRemain84 years 01 month 99297.1 48745.8 2.037 0.041840 *
## LeaseRemain84 years 03 months 155746.9 60436.6 2.577 0.010070 *
## LeaseRemain84 years 04 months 47732.2 49065.2 0.973 0.330810
## LeaseRemain84 years 06 months 32120.8 33562.6 0.957 0.338718
## LeaseRemain84 years 08 months 54899.7 44396.3 1.237 0.216457
## LeaseRemain84 years 09 months 49618.6 29022.3 1.710 0.087556 .
## LeaseRemain84 years 10 months NA NA NA NA
## LeaseRemain84 years 11 months NA NA NA NA
## LeaseRemain85 years 01 month -8162.5 28211.2 -0.289 0.772369
## LeaseRemain85 years 02 months NA NA NA NA
## LeaseRemain85 years 05 months NA NA NA NA
## LeaseRemain85 years 07 months 175028.1 54965.9 3.184 0.001484 **
## LeaseRemain85 years 08 months 207208.6 54527.9 3.800 0.000151 ***
## LeaseRemain85 years 09 months 142422.0 54187.9 2.628 0.008678 **
## LeaseRemain85 years 10 months 190543.8 61812.0 3.083 0.002093 **
## LeaseRemain85 years 11 months 133320.7 49105.9 2.715 0.006713 **
## LeaseRemain86 years 147296.5 50102.3 2.940 0.003339 **
## LeaseRemain86 years 01 month 198774.0 53959.3 3.684 0.000239 ***
## LeaseRemain86 years 02 months 142779.0 45826.3 3.116 0.001874 **
## LeaseRemain86 years 03 months 108422.1 45766.2 2.369 0.017974 *
## LeaseRemain86 years 04 months 119009.5 41579.5 2.862 0.004272 **
## LeaseRemain86 years 05 months 124598.6 42972.5 2.899 0.003798 **
## LeaseRemain86 years 06 months 126001.9 39823.6 3.164 0.001591 **
## LeaseRemain86 years 07 months 114688.4 39298.9 2.918 0.003577 **
## LeaseRemain86 years 08 months 190010.4 45494.8 4.177 3.15e-05 ***
## LeaseRemain86 years 09 months 91368.6 37094.3 2.463 0.013896 *
## LeaseRemain86 years 10 months 127326.4 40185.8 3.168 0.001567 **
## LeaseRemain86 years 11 months 88350.6 35490.6 2.489 0.012915 *
## LeaseRemain87 years 93112.6 34535.2 2.696 0.007101 **
## LeaseRemain87 years 01 month 82571.7 36938.0 2.235 0.025553 *
## LeaseRemain87 years 02 months 46760.1 35215.0 1.328 0.184452
## LeaseRemain87 years 03 months 59483.0 30125.4 1.975 0.048526 *
## LeaseRemain87 years 04 months 36327.9 35292.9 1.029 0.303511
## LeaseRemain87 years 05 months 48434.6 28961.8 1.672 0.094684 .
## LeaseRemain87 years 06 months 183237.0 81159.8 2.258 0.024121 *
## LeaseRemain87 years 07 months 36974.0 32576.1 1.135 0.256575
## LeaseRemain87 years 09 months 204192.8 71560.7 2.853 0.004391 **
## LeaseRemain87 years 11 months 172181.6 77082.7 2.234 0.025664 *
## LeaseRemain88 years NA NA NA NA
## LeaseRemain88 years 01 month 151078.5 57245.8 2.639 0.008408 **
## LeaseRemain88 years 02 months 178220.8 60873.5 2.928 0.003472 **
## LeaseRemain88 years 03 months 146997.1 51321.8 2.864 0.004245 **
## LeaseRemain88 years 04 months 147888.1 53208.4 2.779 0.005521 **
## LeaseRemain88 years 05 months 167269.3 54874.6 3.048 0.002347 **
## LeaseRemain88 years 06 months 159328.5 51097.4 3.118 0.001858 **
## LeaseRemain88 years 07 months 132630.5 50290.8 2.637 0.008453 **
## LeaseRemain88 years 08 months 136409.4 51341.7 2.657 0.007979 **
## LeaseRemain88 years 09 months 115687.3 44113.6 2.622 0.008827 **
## LeaseRemain88 years 10 months 107649.4 48359.6 2.226 0.026177 *
## LeaseRemain88 years 11 months 115373.8 41357.7 2.790 0.005350 **
## LeaseRemain89 years 95658.2 34347.7 2.785 0.005427 **
## LeaseRemain89 years 01 month 95425.6 36268.3 2.631 0.008607 **
## LeaseRemain89 years 02 months 50054.7 38065.6 1.315 0.188746
## LeaseRemain89 years 03 months 68606.5 30061.9 2.282 0.022633 *
## LeaseRemain89 years 04 months 71711.6 29487.4 2.432 0.015147 *
## LeaseRemain89 years 05 months 75159.2 28397.8 2.647 0.008223 **
## LeaseRemain89 years 06 months 68703.5 28508.7 2.410 0.016089 *
## LeaseRemain89 years 07 months 68950.3 25946.2 2.657 0.007966 **
## LeaseRemain89 years 08 months 54615.2 24953.5 2.189 0.028790 *
## LeaseRemain89 years 09 months 49968.4 24587.3 2.032 0.042319 *
## LeaseRemain89 years 10 months 48599.8 24327.6 1.998 0.045947 *
## LeaseRemain89 years 11 months 47443.3 21851.7 2.171 0.030093 *
## LeaseRemain90 years 39302.2 21689.9 1.812 0.070207 .
## LeaseRemain90 years 01 month 38486.8 21829.2 1.763 0.078112 .
## LeaseRemain90 years 02 months 32978.2 19591.0 1.683 0.092540 .
## LeaseRemain90 years 04 months 23697.5 19374.3 1.223 0.221489
## LeaseRemain90 years 05 months 16318.5 22521.5 0.725 0.468838
## LeaseRemain90 years 06 months 29084.1 26127.8 1.113 0.265842
## LeaseRemain90 years 07 months NA NA NA NA
## LeaseRemain90 years 08 months 260349.5 87180.9 2.986 0.002874 **
## LeaseRemain90 years 09 months 260246.1 89200.9 2.918 0.003586 **
## LeaseRemain90 years 11 months 256348.6 88103.3 2.910 0.003678 **
## LeaseRemain91 years 249977.9 81941.6 3.051 0.002328 **
## LeaseRemain91 years 01 month 255037.0 79481.8 3.209 0.001364 **
## LeaseRemain91 years 02 months 255307.1 78056.0 3.271 0.001099 **
## LeaseRemain91 years 03 months 255401.8 80424.9 3.176 0.001529 **
## LeaseRemain91 years 04 months 250298.1 75169.3 3.330 0.000892 ***
## LeaseRemain91 years 05 months 253094.2 73871.0 3.426 0.000631 ***
## LeaseRemain91 years 06 months 242598.0 72029.9 3.368 0.000778 ***
## LeaseRemain91 years 07 months 235473.6 70678.7 3.332 0.000887 ***
## LeaseRemain91 years 08 months 241540.8 69757.5 3.463 0.000552 ***
## LeaseRemain91 years 09 months 221764.8 68013.3 3.261 0.001139 **
## LeaseRemain91 years 10 months 236604.6 67005.0 3.531 0.000428 ***
## LeaseRemain91 years 11 months 229205.5 65707.3 3.488 0.000502 ***
## LeaseRemain92 years 230143.1 63926.9 3.600 0.000330 ***
## LeaseRemain92 years 01 month 212874.9 62969.9 3.381 0.000744 ***
## LeaseRemain92 years 02 months 210340.7 61497.1 3.420 0.000644 ***
## LeaseRemain92 years 03 months 209203.1 60228.8 3.473 0.000530 ***
## LeaseRemain92 years 04 months 193956.3 58945.7 3.290 0.001026 **
## LeaseRemain92 years 05 months 192731.9 57571.2 3.348 0.000837 ***
## LeaseRemain92 years 06 months 180248.8 56706.9 3.179 0.001513 **
## LeaseRemain92 years 07 months 179204.0 55083.3 3.253 0.001169 **
## LeaseRemain92 years 08 months 174156.5 53832.9 3.235 0.001245 **
## LeaseRemain92 years 09 months 169729.1 53301.2 3.184 0.001484 **
## LeaseRemain92 years 10 months 156142.6 51184.7 3.051 0.002328 **
## LeaseRemain92 years 11 months 154266.0 50210.9 3.072 0.002166 **
## LeaseRemain93 years 151152.2 48904.0 3.091 0.002037 **
## LeaseRemain93 years 01 month 154763.9 47725.1 3.243 0.001212 **
## LeaseRemain93 years 02 months 149786.7 46394.4 3.229 0.001274 **
## LeaseRemain93 years 03 months 144847.1 45546.0 3.180 0.001505 **
## LeaseRemain93 years 04 months 129777.3 44263.0 2.932 0.003425 **
## LeaseRemain93 years 05 months 135808.0 42840.3 3.170 0.001558 **
## LeaseRemain93 years 06 months 121350.7 41402.7 2.931 0.003436 **
## LeaseRemain93 years 07 months 113865.4 40450.7 2.815 0.004950 **
## LeaseRemain93 years 08 months 110442.0 39649.9 2.785 0.005420 **
## LeaseRemain93 years 09 months 103354.2 38699.1 2.671 0.007660 **
## LeaseRemain93 years 10 months 104672.5 37482.5 2.793 0.005303 **
## LeaseRemain93 years 11 months 99525.2 36567.7 2.722 0.006579 **
## LeaseRemain94 years 76572.4 34918.4 2.193 0.028485 *
## LeaseRemain94 years 01 month 89373.6 33975.3 2.631 0.008621 **
## LeaseRemain94 years 02 months 71068.8 33435.5 2.126 0.033721 *
## LeaseRemain94 years 03 months 73767.6 31899.9 2.312 0.020901 *
## LeaseRemain94 years 04 months 68688.7 31042.1 2.213 0.027081 *
## LeaseRemain94 years 05 months 66417.4 30599.9 2.171 0.030141 *
## LeaseRemain94 years 06 months 60837.4 29391.3 2.070 0.038650 *
## LeaseRemain94 years 07 months 57954.2 28779.4 2.014 0.044234 *
## LeaseRemain94 years 08 months 56748.4 27882.9 2.035 0.042021 *
## LeaseRemain94 years 09 months 51267.8 27189.3 1.886 0.059564 .
## LeaseRemain94 years 10 months 52711.6 26684.4 1.975 0.048429 *
## LeaseRemain94 years 11 months 38509.6 26235.1 1.468 0.142373
## LeaseRemain95 years 30487.6 25856.9 1.179 0.238569
## LeaseRemain95 years 01 month 30637.7 25605.2 1.197 0.231694
## LeaseRemain95 years 02 months 60046.8 25337.9 2.370 0.017935 *
## LeaseRemain95 years 03 months 40800.5 32685.0 1.248 0.212138
## LeaseRemain95 years 04 months 31607.2 32402.8 0.975 0.329512
## LeaseRemain95 years 05 months NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22860 on 1354 degrees of freedom
## Multiple R-squared: 0.9549, Adjusted R-squared: 0.9296
## F-statistic: 37.71 on 761 and 1354 DF, p-value: < 2.2e-16From the regression above, we know that there are too many categorical variables to consider. We have to condense them accordingly. Since we have visualised each block on the map and designate their respective subzone. We can categorise them in this manner as each neighborhood will have close proximity to their own respective facilities, such as schools, malls, childcare centre, etc. We can then see which subzones relative effects and it can show which subzone is more popular or less popular. In addition, it will help reduce the perfect collinearity issue that this current regression has.
length(unique(Sengkang$Block))## [1] 521length(unique(Sengkang$Street))## [1] 29length(unique(Sengkang$LeaseRemain))## [1] 226We can see from the code chunk above that block, street and LeaseRemain has 521, 29 and 226 categorical variables.
Data Wrangling
We will use the lubridate package to adjust the year and calculate lease years used as a numeric rather than a categorical variable. Since years_used and LeaseRemain are perfected correlated, we will drop LeaseRemaind from the dataframe.
site, the HDB blocks are numbered by 100+, 200+, 300+ and 400+ in Rivervale, Compassvale, Anchorvale and Fernvale respectively.
df <- Sengkang1 %>%
mutate(Date = lubridate::ym(Date),
LeaseBegin = lubridate::ym( paste0(LeaseBegin,"-01")),
years_used = as.numeric((Date - LeaseBegin)/365),
subzone = ifelse(grepl("^1", Block), "Rivervale",
ifelse(grepl("^2", Block), "Compassvale",
ifelse(grepl("^3", Block), "Anchorvale",
ifelse(grepl("4", Block), "Fernvale", "others")))),
.before = Street) %>%
mutate(subzone= as.factor(subzone),
Date = as.factor(Date)) %>%
select(-LeaseRemain, -LeaseBegin)Using leaseremain as a factor will generate too many binary variables. Convert them into years_used would be easier. Date and LeaseBegin variables must be in date type before substracting between the two. The output would be in (drtn) days and thus we have to set it to numeric set to years.
Find the relationship between independent variables and Resale Price
plot(df$Date, df$ResalePrice)
plot(df$Type, df$ResalePrice)
plot(df$Block, df$ResalePrice)
plot(df$years_used, df$ResalePrice)
plot(df$subzone, df$ResalePrice)
plot(df$Street, df$ResalePrice)
plot(df$Story, df$ResalePrice)
plot(df$Area, log(df$ResalePrice))
plot(df$Model, df$ResalePrice)
Run Regression
All variables
We will first calculate the BIC of the regression of all variables.
reg_all <- lm(ResalePrice ~ ., data = df)
BIC(reg_all)## [1] 52085.02Residual check
r <- residuals(reg_all)
plot(df$Date, r,
xlab = "Date", ylab = "Residuals")
plot(df$Type, r,
xlab = "Type", ylab = "Residuals")
plot(df$Block, r,
xlab = "Block", ylab = "Residuals")
plot(df$years_used, r,
xlab = "years_used", ylab = "Residuals")
plot(df$subzone, r,
xlab = "subzone", ylab = "Residuals")
plot(df$Street, r,
xlab = "Street", ylab = "Residuals")
plot(df$Story, r,
xlab = "Story", ylab = "Residuals")
plot(df$Area, r,
xlab = "Area", ylab = "Residuals")
plot(df$Model, r,
xlab = "Model", ylab = "Residuals")
From the residual plots above, we notice all plots points are scattered
around the residual =0. This suggesrt that the model assumptions are not
violated. We have three types of location columns now, Block, Street and
subzone. There should be high correlation between the X variables for
these 3 variables, we will test the BIC number by dropping each variable
out and picking the model with the lowest BIC ## Removing Block
L1 <- lm(ResalePrice ~ .-Block, data = df)
summary(L1)##
## Call:
## lm(formula = ResalePrice ~ . - Block, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -125199 -18458 -391 16605 127493
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 210695.6 22823.2 9.232 < 2e-16 ***
## Date2022-02-01 3068.6 3127.6 0.981 0.326637
## Date2022-03-01 9561.5 3012.4 3.174 0.001525 **
## Date2022-04-01 19707.9 2957.8 6.663 3.43e-11 ***
## Date2022-05-01 22649.6 3022.6 7.493 9.91e-14 ***
## Date2022-06-01 30197.7 3101.4 9.737 < 2e-16 ***
## Date2022-07-01 34030.9 2899.1 11.738 < 2e-16 ***
## Date2022-08-01 35921.4 2959.2 12.139 < 2e-16 ***
## Date2022-09-01 46776.8 2968.3 15.759 < 2e-16 ***
## Date2022-10-01 54208.3 3198.9 16.946 < 2e-16 ***
## Date2022-11-01 56573.0 3172.8 17.831 < 2e-16 ***
## Date2022-12-01 63968.7 3084.1 20.742 < 2e-16 ***
## Type4 ROOM 49589.9 8541.6 5.806 7.41e-09 ***
## Type5 ROOM 111718.7 14907.3 7.494 9.85e-14 ***
## years_used -7932.9 170.6 -46.503 < 2e-16 ***
## subzoneCompassvale 41771.1 8999.2 4.642 3.67e-06 ***
## subzoneFernvale -19184.9 4668.2 -4.110 4.12e-05 ***
## subzoneRivervale -34282.0 8746.1 -3.920 9.16e-05 ***
## StreetANCHORVALE DR 31753.6 6185.3 5.134 3.11e-07 ***
## StreetANCHORVALE LANE -12441.5 7709.0 -1.614 0.106706
## StreetANCHORVALE LINK 12221.1 4386.9 2.786 0.005388 **
## StreetANCHORVALE RD -361.1 4641.1 -0.078 0.937990
## StreetANCHORVALE ST 4879.3 5521.0 0.884 0.376923
## StreetCOMPASSVALE BOW 49697.4 10253.2 4.847 1.35e-06 ***
## StreetCOMPASSVALE CRES -35722.9 9568.3 -3.733 0.000194 ***
## StreetCOMPASSVALE DR 31509.0 9913.0 3.179 0.001502 **
## StreetCOMPASSVALE LANE -31117.6 9936.8 -3.132 0.001763 **
## StreetCOMPASSVALE LINK 65221.1 10239.0 6.370 2.33e-10 ***
## StreetCOMPASSVALE RD 5531.1 10588.8 0.522 0.601478
## StreetCOMPASSVALE ST -34202.2 10359.9 -3.301 0.000978 ***
## StreetCOMPASSVALE WALK 2385.9 10932.0 0.218 0.827260
## StreetFERNVALE LANE 11616.4 7948.8 1.461 0.144058
## StreetFERNVALE LINK 8008.5 4145.7 1.932 0.053525 .
## StreetFERNVALE RD 19886.0 4575.1 4.347 1.45e-05 ***
## StreetFERNVALE ST 6151.8 6283.4 0.979 0.327671
## StreetJLN KAYU 6159.1 9980.8 0.617 0.537240
## StreetRIVERVALE CRES 10162.6 9429.7 1.078 0.281284
## StreetRIVERVALE DR 46191.2 9828.5 4.700 2.78e-06 ***
## StreetRIVERVALE ST 48896.7 11317.6 4.320 1.63e-05 ***
## StreetRIVERVALE WALK 73305.2 11396.4 6.432 1.56e-10 ***
## StreetSENGKANG CTRL 70136.4 10972.0 6.392 2.02e-10 ***
## StreetSENGKANG EAST AVE 66487.3 10535.5 6.311 3.39e-10 ***
## StreetSENGKANG EAST RD 1205.1 13776.8 0.087 0.930305
## StreetSENGKANG EAST WAY 46129.6 6596.5 6.993 3.62e-12 ***
## StreetSENGKANG WEST AVE 31509.1 9286.4 3.393 0.000704 ***
## StreetSENGKANG WEST WAY NA NA NA NA
## Story04 TO 06 25592.7 2314.5 11.058 < 2e-16 ***
## Story07 TO 09 42931.7 2287.7 18.767 < 2e-16 ***
## Story10 TO 12 48919.7 2365.3 20.682 < 2e-16 ***
## Story13 TO 15 57804.1 2288.3 25.261 < 2e-16 ***
## Story16 TO 18 66014.4 2852.9 23.139 < 2e-16 ***
## Story19 TO 21 62481.2 4257.8 14.674 < 2e-16 ***
## Story22 TO 24 70526.8 4802.6 14.685 < 2e-16 ***
## Story25 TO 27 64799.3 6652.8 9.740 < 2e-16 ***
## Area 2752.4 327.1 8.413 < 2e-16 ***
## ModelModel A 10424.3 2968.2 3.512 0.000454 ***
## ModelModel A2 52537.4 5374.8 9.775 < 2e-16 ***
## ModelPremium Apartment 20248.3 2601.4 7.784 1.11e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29140 on 2059 degrees of freedom
## Multiple R-squared: 0.8887, Adjusted R-squared: 0.8857
## F-statistic: 293.6 on 56 and 2059 DF, p-value: < 2.2e-16Removing Street
L2 <- lm(ResalePrice ~ .-Street,
data = df)
summary(L2)##
## Call:
## lm(formula = ResalePrice ~ . - Street, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -108099 -10797 0 11327 83503
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 57717.8 56921.9 1.014 0.310747
## Date2022-02-01 3205.0 2814.8 1.139 0.255040
## Date2022-03-01 6466.2 2705.6 2.390 0.016970 *
## Date2022-04-01 17158.8 2692.6 6.373 2.44e-10 ***
## Date2022-05-01 18814.9 2712.3 6.937 5.84e-12 ***
## Date2022-06-01 25490.1 2826.4 9.018 < 2e-16 ***
## Date2022-07-01 28758.1 2614.3 11.000 < 2e-16 ***
## Date2022-08-01 31702.8 2674.3 11.855 < 2e-16 ***
## Date2022-09-01 40950.6 2693.9 15.201 < 2e-16 ***
## Date2022-10-01 45604.4 2955.5 15.430 < 2e-16 ***
## Date2022-11-01 52303.1 2884.9 18.130 < 2e-16 ***
## Date2022-12-01 53873.6 2829.7 19.039 < 2e-16 ***
## Type4 ROOM 44773.9 18376.4 2.436 0.014941 *
## Type5 ROOM 109528.5 32417.7 3.379 0.000746 ***
## Block104 38496.4 28571.1 1.347 0.178050
## Block105 29117.8 20223.1 1.440 0.150115
## Block106 12158.8 21354.2 0.569 0.569176
## Block107 20476.7 19467.4 1.052 0.293034
## Block108 22050.0 23269.1 0.948 0.343474
## Block109 -5928.6 19034.0 -0.311 0.755482
## Block112 36912.5 28595.6 1.291 0.196946
## Block113 9837.5 28592.5 0.344 0.730847
## Block114 23623.2 23352.6 1.012 0.311891
## Block115 -3738.4 21281.9 -0.176 0.860583
## Block116A 7067.1 23750.3 0.298 0.766082
## Block116B 15253.1 28877.6 0.528 0.597437
## Block116C 19600.5 23678.2 0.828 0.407918
## Block117A 30498.8 28900.2 1.055 0.291444
## Block117B 6985.0 28797.4 0.243 0.808381
## Block117C -8221.0 21710.6 -0.379 0.704988
## Block119A 76515.9 28645.3 2.671 0.007637 **
## Block119D 39860.5 28698.0 1.389 0.165040
## Block120A 41046.0 28708.4 1.430 0.152986
## Block120B 49664.9 28669.6 1.732 0.083413 .
## Block121 -3589.3 20243.1 -0.177 0.859287
## Block121A 2548.2 21621.5 0.118 0.906198
## Block121C 218.0 21571.1 0.010 0.991938
## Block121D -2607.4 21057.2 -0.124 0.901472
## Block122 -17958.3 21572.7 -0.832 0.405280
## Block122A -5613.1 20845.0 -0.269 0.787750
## Block122D -8490.3 29604.6 -0.287 0.774312
## Block122E -18036.5 21132.1 -0.854 0.393506
## Block123 -12474.1 19622.4 -0.636 0.525060
## Block123A 23734.7 28569.0 0.831 0.406221
## Block123B -23287.1 20364.5 -1.144 0.252998
## Block123C -8667.4 28693.4 -0.302 0.762640
## Block123D -16957.1 23692.2 -0.716 0.474268
## Block123E -41107.1 28840.9 -1.425 0.154267
## Block124 806.2 23300.2 0.035 0.972401
## Block124A 175.7 19451.8 0.009 0.992794
## Block124B 52519.1 22812.8 2.302 0.021455 *
## Block124C 35324.0 22788.4 1.550 0.121323
## Block125 -11127.2 20107.0 -0.553 0.580069
## Block126 10652.7 23343.7 0.456 0.648207
## Block128 -7316.3 20149.9 -0.363 0.716583
## Block129 -20893.8 28547.0 -0.732 0.464333
## Block131 36484.8 24171.7 1.509 0.131398
## Block132 -9076.1 19508.1 -0.465 0.641818
## Block133 -18675.4 20151.6 -0.927 0.354201
## Block134 -7830.2 21296.6 -0.368 0.713167
## Block140 13519.9 29420.2 0.460 0.645907
## Block141 -6702.0 21264.9 -0.315 0.752676
## Block142 -35326.5 23351.0 -1.513 0.130520
## Block145 12061.7 28564.9 0.422 0.672897
## Block146 -21015.1 28571.8 -0.736 0.462134
## Block148 -9783.0 21351.5 -0.458 0.646882
## Block150 34188.8 24566.5 1.392 0.164214
## Block151 16700.0 20909.6 0.799 0.424598
## Block152 17609.9 22641.8 0.778 0.436829
## Block153 41538.5 21584.6 1.924 0.054478 .
## Block154 39028.0 29534.1 1.321 0.186541
## Block155 22715.0 24612.2 0.923 0.356193
## Block156 40167.4 22615.3 1.776 0.075908 .
## Block157A 109.1 19773.7 0.006 0.995599
## Block157B 45583.9 20930.1 2.178 0.029561 *
## Block157C 3749.8 24503.7 0.153 0.878396
## Block157D 11478.4 21209.9 0.541 0.588458
## Block158A -2289.1 21490.5 -0.107 0.915184
## Block158B -23123.0 24311.6 -0.951 0.341695
## Block158C -5475.9 20581.2 -0.266 0.790225
## Block158D 26833.8 24024.4 1.117 0.264191
## Block159A 34076.8 21541.9 1.582 0.113878
## Block162A 87940.9 19513.4 4.507 7.07e-06 ***
## Block162B 77576.7 19889.7 3.900 0.000100 ***
## Block162C 70866.9 20276.7 3.495 0.000487 ***
## Block163A 69773.3 19530.6 3.573 0.000364 ***
## Block163B 95744.0 21997.4 4.353 1.43e-05 ***
## Block163C 69544.6 22080.1 3.150 0.001665 **
## Block164A 73225.1 19837.1 3.691 0.000231 ***
## Block164B 89201.0 20390.9 4.375 1.30e-05 ***
## Block164C 73540.3 20320.6 3.619 0.000305 ***
## Block178A 56712.7 22036.5 2.574 0.010156 *
## Block178B 35053.8 19306.2 1.816 0.069612 .
## Block178C 59347.9 19574.9 3.032 0.002470 **
## Block178D 33431.1 29125.0 1.148 0.251207
## Block180A 75002.5 24250.5 3.093 0.002017 **
## Block180B 88954.2 20672.0 4.303 1.79e-05 ***
## Block180C 39599.1 19317.5 2.050 0.040540 *
## Block180D 76942.2 20669.3 3.723 0.000204 ***
## Block183A -24440.3 21031.2 -1.162 0.245372
## Block183B 22273.0 29643.8 0.751 0.452553
## Block183C -19923.7 21659.4 -0.920 0.357785
## Block183D 33717.7 22445.2 1.502 0.133241
## Block184A -3530.9 24580.2 -0.144 0.885797
## Block184B -31621.2 29588.1 -1.069 0.285363
## Block184C 32988.9 24264.9 1.360 0.174173
## Block185A 3642.2 24588.9 0.148 0.882264
## Block185B 24153.1 24335.8 0.992 0.321110
## Block185C 39713.5 23522.7 1.688 0.091550 .
## Block185D 40387.3 22196.8 1.820 0.069024 .
## Block186A -28361.0 24688.9 -1.149 0.250840
## Block186B -29657.2 21605.3 -1.373 0.170047
## Block186C 7396.4 21625.4 0.342 0.732378
## Block186D 1727.3 29451.9 0.059 0.953238
## Block187B -38745.3 24554.3 -1.578 0.114781
## Block188B -5514.7 20500.3 -0.269 0.787961
## Block188C -47426.3 23695.6 -2.001 0.045512 *
## Block188D -33069.0 20599.9 -1.605 0.108629
## Block190A -399.3 23603.2 -0.017 0.986505
## Block190B 14717.0 21687.4 0.679 0.497493
## Block191B -9600.5 23755.2 -0.404 0.686162
## Block192A 45345.8 23652.7 1.917 0.055400 .
## Block192B -15033.9 28878.8 -0.521 0.602730
## Block192C -6398.5 23709.4 -0.270 0.787294
## Block193 -2958.7 20758.4 -0.143 0.886680
## Block194 3513.8 21429.9 0.164 0.869777
## Block195 14105.4 24403.9 0.578 0.563348
## Block196 -6875.3 21408.4 -0.321 0.748141
## Block197 -2528.8 20278.0 -0.125 0.900771
## Block200A 30078.5 21002.0 1.432 0.152293
## Block200B 20152.7 29601.7 0.681 0.496101
## Block201A 15479.2 29578.4 0.523 0.600820
## Block201B 49480.2 22692.8 2.180 0.029373 *
## Block201C 41883.3 24581.8 1.704 0.088610 .
## Block201D 29470.9 22668.4 1.300 0.193761
## Block202 52459.3 26165.4 2.005 0.045143 *
## Block202C 43756.9 22659.9 1.931 0.053659 .
## Block203B 40384.1 24615.6 1.641 0.101082
## Block203C 28477.3 22634.2 1.258 0.208523
## Block203E 20204.1 22674.4 0.891 0.373037
## Block204A 27431.9 24587.3 1.116 0.264724
## Block204B 33889.0 22613.8 1.499 0.134179
## Block204C 19192.8 29617.7 0.648 0.517069
## Block205C -368.4 21299.2 -0.017 0.986202
## Block206A 3084.5 28582.0 0.108 0.914075
## Block206B 3848.8 20257.6 0.190 0.849338
## Block206C 5277.5 20230.9 0.261 0.794232
## Block206D 4953.2 23303.6 0.213 0.831704
## Block207A 29971.6 24190.9 1.239 0.215546
## Block207B 32955.7 22492.2 1.465 0.143065
## Block207C 3669.0 29543.6 0.124 0.901180
## Block207D 47514.0 24939.3 1.905 0.056938 .
## Block208A 100577.7 22259.2 4.518 6.69e-06 ***
## Block208B 89075.1 20513.5 4.342 1.50e-05 ***
## Block209A 75695.8 21181.3 3.574 0.000363 ***
## Block209B 92043.3 24337.7 3.782 0.000161 ***
## Block209C 100094.7 21253.0 4.710 2.70e-06 ***
## Block210A 87386.0 19277.1 4.533 6.25e-06 ***
## Block210B 83437.9 20286.6 4.113 4.11e-05 ***
## Block210C 92157.7 22033.3 4.183 3.04e-05 ***
## Block211A 101753.5 19789.7 5.142 3.06e-07 ***
## Block211B 86253.1 21007.4 4.106 4.24e-05 ***
## Block211C 92884.4 18524.5 5.014 5.93e-07 ***
## Block211D 88759.2 19185.3 4.626 4.03e-06 ***
## Block212A 77728.5 21815.1 3.563 0.000377 ***
## Block212B 108366.8 21487.0 5.043 5.10e-07 ***
## Block212C 89459.2 21932.8 4.079 4.75e-05 ***
## Block213A 95698.5 21546.5 4.441 9.56e-06 ***
## Block213B 79311.0 19570.5 4.053 5.31e-05 ***
## Block215A 199889.4 19315.6 10.349 < 2e-16 ***
## Block215B 234050.4 19826.9 11.805 < 2e-16 ***
## Block216A 269243.0 20613.6 13.061 < 2e-16 ***
## Block216B 282925.9 19564.6 14.461 < 2e-16 ***
## Block216C 275487.4 24250.6 11.360 < 2e-16 ***
## Block216D 241195.5 19847.1 12.153 < 2e-16 ***
## Block217A 234767.4 20672.5 11.356 < 2e-16 ***
## Block217B 186543.6 20642.6 9.037 < 2e-16 ***
## Block217C 259604.7 20147.2 12.885 < 2e-16 ***
## Block223B 24989.0 28548.9 0.875 0.381541
## Block223C 10375.1 23342.5 0.444 0.656764
## Block223D 42521.6 21281.5 1.998 0.045882 *
## Block224B 29394.8 21289.8 1.381 0.167567
## Block224C 42861.8 28465.3 1.506 0.132331
## Block224D 40313.0 21340.8 1.889 0.059074 .
## Block225A 15231.9 28542.1 0.534 0.593649
## Block225B 4901.4 21484.1 0.228 0.819566
## Block226A -6867.8 28554.7 -0.241 0.809963
## Block226B 20008.0 21337.9 0.938 0.348555
## Block227A 50265.3 28584.6 1.758 0.078862 .
## Block227C -2237.6 21365.9 -0.105 0.916606
## Block227D 25589.3 28529.8 0.897 0.369892
## Block228A -18834.6 23720.6 -0.794 0.427303
## Block228B 33269.3 19493.3 1.707 0.088075 .
## Block228C -9427.9 23725.2 -0.397 0.691142
## Block229 -10554.5 21322.0 -0.495 0.620665
## Block230 2938.9 21250.7 0.138 0.890024
## Block231 33247.5 23315.3 1.426 0.154069
## Block232 18873.9 23320.6 0.809 0.418452
## Block235 36243.2 23349.7 1.552 0.120817
## Block236 2548.1 21366.6 0.119 0.905087
## Block237 24801.1 20206.9 1.227 0.219873
## Block238 30008.9 20172.3 1.488 0.137049
## Block239 38828.8 28571.8 1.359 0.174344
## Block240 34253.7 28464.4 1.203 0.229009
## Block241 22964.2 28506.8 0.806 0.420612
## Block244 -8385.0 23577.0 -0.356 0.722154
## Block245 -7455.3 23577.2 -0.316 0.751887
## Block246 55294.1 21610.0 2.559 0.010598 *
## Block247 82054.6 25412.6 3.229 0.001268 **
## Block248 5634.6 28793.6 0.196 0.844878
## Block251 -29353.6 23627.2 -1.242 0.214288
## Block253 -13889.5 28870.8 -0.481 0.630518
## Block255 -16464.3 21562.8 -0.764 0.445248
## Block257A 39037.7 24587.5 1.588 0.112554
## Block257B 126430.6 25415.1 4.975 7.25e-07 ***
## Block257C 58627.5 24542.1 2.389 0.017018 *
## Block258A 67939.0 22658.4 2.998 0.002757 **
## Block258B 60081.1 22684.0 2.649 0.008163 **
## Block258C 41140.1 21630.0 1.902 0.057355 .
## Block258D 50711.5 21017.0 2.413 0.015941 *
## Block259A 40514.5 29613.5 1.368 0.171473
## Block259B 71186.1 26150.2 2.722 0.006556 **
## Block259C 39999.0 29599.1 1.351 0.176774
## Block260A 106882.8 22647.9 4.719 2.58e-06 ***
## Block260B 101399.7 29541.7 3.432 0.000614 ***
## Block260C 54778.8 21666.5 2.528 0.011560 *
## Block260D 110941.5 24578.0 4.514 6.84e-06 ***
## Block261A 57022.0 21642.2 2.635 0.008502 **
## Block261B 63865.8 24553.9 2.601 0.009381 **
## Block261C 132499.4 29707.3 4.460 8.77e-06 ***
## Block262A 38339.6 20560.2 1.865 0.062403 .
## Block262D 18712.2 24585.1 0.761 0.446699
## Block264A 115974.3 24367.7 4.759 2.12e-06 ***
## Block264B 141542.2 24367.1 5.809 7.60e-09 ***
## Block264C 162392.9 29428.5 5.518 4.00e-08 ***
## Block264D 170407.9 29420.2 5.792 8.37e-09 ***
## Block264E 155671.0 24333.9 6.397 2.08e-10 ***
## Block264F 176973.6 29322.9 6.035 1.97e-09 ***
## Block265A 200390.2 29428.8 6.809 1.39e-11 ***
## Block265B 147994.6 29409.7 5.032 5.41e-07 ***
## Block265C 121753.4 21397.3 5.690 1.51e-08 ***
## Block265D 157795.0 20278.5 7.781 1.29e-14 ***
## Block266A 155337.6 21406.3 7.257 6.21e-13 ***
## Block266B 178544.1 29391.6 6.075 1.56e-09 ***
## Block267A 140230.7 24834.1 5.647 1.94e-08 ***
## Block267B 112017.1 21210.9 5.281 1.46e-07 ***
## Block268A 134666.7 29525.8 4.561 5.49e-06 ***
## Block268B 151842.4 29771.2 5.100 3.80e-07 ***
## Block268C 111732.5 21092.4 5.297 1.34e-07 ***
## Block268D 133441.1 24667.3 5.410 7.29e-08 ***
## Block269A 123889.4 21737.9 5.699 1.43e-08 ***
## Block269B 143767.4 29797.7 4.825 1.54e-06 ***
## Block269C 99483.6 29745.8 3.344 0.000844 ***
## Block269D 112333.7 21088.5 5.327 1.14e-07 ***
## Block270A 163651.3 22216.1 7.366 2.82e-13 ***
## Block271A 179836.6 20485.3 8.779 < 2e-16 ***
## Block271B 157754.8 22203.8 7.105 1.82e-12 ***
## Block271C 190500.4 19722.4 9.659 < 2e-16 ***
## Block272A 223425.1 24757.0 9.025 < 2e-16 ***
## Block272B 211307.7 22887.2 9.233 < 2e-16 ***
## Block272C 235304.2 22889.0 10.280 < 2e-16 ***
## Block272D 213010.4 22908.5 9.298 < 2e-16 ***
## Block273B 169197.1 29693.1 5.698 1.44e-08 ***
## Block273C 241541.1 29797.3 8.106 1.04e-15 ***
## Block273D 224518.9 21214.4 10.583 < 2e-16 ***
## Block274A 203215.8 19654.0 10.340 < 2e-16 ***
## Block274B 210527.3 20957.6 10.045 < 2e-16 ***
## Block274C 228605.9 21225.8 10.770 < 2e-16 ***
## Block275A 207795.0 21747.7 9.555 < 2e-16 ***
## Block275B 201715.7 22854.1 8.826 < 2e-16 ***
## Block275C 228017.4 21738.2 10.489 < 2e-16 ***
## Block275D 223274.4 24542.3 9.098 < 2e-16 ***
## Block277A 237515.9 21148.4 11.231 < 2e-16 ***
## Block277B 207647.9 24742.4 8.392 < 2e-16 ***
## Block277C 235490.5 22721.7 10.364 < 2e-16 ***
## Block277D 217795.4 22869.5 9.523 < 2e-16 ***
## Block278A 212879.0 21060.8 10.108 < 2e-16 ***
## Block278B 209188.8 19385.6 10.791 < 2e-16 ***
## Block278C 186153.0 21174.4 8.791 < 2e-16 ***
## Block279A 170601.4 29512.5 5.781 8.96e-09 ***
## Block279B 265811.3 20562.4 12.927 < 2e-16 ***
## Block279C 147568.3 24474.7 6.029 2.05e-09 ***
## Block280A 218205.7 22192.9 9.832 < 2e-16 ***
## Block280B 205914.2 21375.3 9.633 < 2e-16 ***
## Block281A 193703.7 20746.7 9.337 < 2e-16 ***
## Block281B 221507.1 20732.3 10.684 < 2e-16 ***
## Block282B 256403.9 20148.0 12.726 < 2e-16 ***
## Block282C 265148.3 19527.1 13.578 < 2e-16 ***
## Block286A 129417.7 18979.8 6.819 1.31e-11 ***
## Block286B 140177.6 18393.3 7.621 4.32e-14 ***
## Block286C 141772.7 18693.6 7.584 5.70e-14 ***
## Block287A 144932.0 18237.6 7.947 3.62e-15 ***
## Block287B 139903.6 19604.9 7.136 1.46e-12 ***
## Block287C 140404.4 18399.9 7.631 4.02e-14 ***
## Block288A 147115.8 18327.8 8.027 1.94e-15 ***
## Block288B 151291.2 18886.5 8.011 2.20e-15 ***
## Block288C 135862.4 18347.2 7.405 2.13e-13 ***
## Block289A 157307.3 18037.4 8.721 < 2e-16 ***
## Block289B 140295.3 18298.0 7.667 3.06e-14 ***
## Block290A 33273.2 24551.4 1.355 0.175533
## Block290B 2960.5 21606.2 0.137 0.891033
## Block290C -11680.4 24549.4 -0.476 0.634287
## Block291A 6231.4 29564.0 0.211 0.833090
## Block291B 11440.2 24598.8 0.465 0.641945
## Block291D 11047.5 21024.0 0.525 0.599329
## Block292A 9059.0 22678.6 0.399 0.689616
## Block292B 12089.1 20548.8 0.588 0.556409
## Block293A 127150.0 18907.7 6.725 2.45e-11 ***
## Block293B 131210.1 18936.9 6.929 6.17e-12 ***
## Block293C 121682.2 19086.5 6.375 2.39e-10 ***
## Block293D 133481.4 19508.9 6.842 1.11e-11 ***
## Block294A 118923.0 19919.6 5.970 2.92e-09 ***
## Block295A -12790.3 20241.4 -0.632 0.527554
## Block295B -25933.5 21011.9 -1.234 0.217302
## Block295C 28334.2 22652.4 1.251 0.211184
## Block296A -2695.9 22691.2 -0.119 0.905444
## Block296B 7768.2 22584.2 0.344 0.730916
## Block296C -4978.5 24572.8 -0.203 0.839472
## Block297A 15030.2 29085.3 0.517 0.605394
## Block297B 16439.3 22082.8 0.744 0.456721
## Block298A 9256.4 19536.0 0.474 0.635699
## Block298B 42330.9 22016.3 1.923 0.054697 .
## Block298C 11613.6 21932.6 0.530 0.596524
## Block298D 466.0 19402.0 0.024 0.980842
## Block299A -8661.2 19737.6 -0.439 0.660855
## Block299B -1734.4 23474.4 -0.074 0.941111
## Block299C 6590.4 23850.4 0.276 0.782337
## Block301A 45119.4 29564.0 1.526 0.127171
## Block301B 26209.5 21605.4 1.213 0.225274
## Block301C -10065.4 22651.4 -0.444 0.656842
## Block301D 9037.7 24562.4 0.368 0.712960
## Block302A -457.4 29604.6 -0.015 0.987675
## Block302B 57185.7 21322.2 2.682 0.007395 **
## Block303A 6393.3 24577.1 0.260 0.794796
## Block303B 55995.8 22488.0 2.490 0.012876 *
## Block303C 50962.8 23341.3 2.183 0.029156 *
## Block304A 21252.5 22691.7 0.937 0.349121
## Block304B 10615.4 22643.9 0.469 0.639278
## Block305A 5846.4 22636.3 0.258 0.796230
## Block305B -14107.3 22668.6 -0.622 0.533816
## Block305C -8971.5 24594.2 -0.365 0.715324
## Block306A 9862.1 21623.8 0.456 0.648399
## Block306C 7154.5 20995.1 0.341 0.733323
## Block307A -20991.8 21653.3 -0.969 0.332469
## Block307C 5968.4 24521.1 0.243 0.807729
## Block308A -18656.1 29543.7 -0.631 0.527821
## Block308B 818.6 22675.7 0.036 0.971207
## Block308C -7924.9 20554.3 -0.386 0.699876
## Block309A 60081.7 29694.0 2.023 0.043205 *
## Block309B 23973.5 20581.1 1.165 0.244263
## Block309C 49900.9 24203.6 2.062 0.039399 *
## Block309D 39364.9 21099.3 1.866 0.062270 .
## Block310B 6635.3 24387.9 0.272 0.785601
## Block311A 10328.2 20000.7 0.516 0.605653
## Block311B 8107.2 24446.4 0.332 0.740213
## Block311C 499.0 21298.1 0.023 0.981310
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## years_used NA NA NA NA
## subzoneCompassvale NA NA NA NA
## subzoneFernvale NA NA NA NA
## subzoneRivervale NA NA NA NA
## Story04 TO 06 26312.9 2131.9 12.342 < 2e-16 ***
## Story07 TO 09 46673.6 2085.4 22.381 < 2e-16 ***
## Story10 TO 12 51697.7 2153.0 24.012 < 2e-16 ***
## Story13 TO 15 59526.1 2077.3 28.656 < 2e-16 ***
## Story16 TO 18 72345.8 2615.8 27.658 < 2e-16 ***
## Story19 TO 21 67441.6 3790.2 17.794 < 2e-16 ***
## Story22 TO 24 76668.2 4256.8 18.011 < 2e-16 ***
## Story25 TO 27 77270.0 5886.0 13.128 < 2e-16 ***
## Area 2717.3 716.2 3.794 0.000154 ***
## ModelModel A 13380.1 3093.3 4.326 1.62e-05 ***
## ModelModel A2 NA NA NA NA
## ModelPremium Apartment NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23180 on 1572 degrees of freedom
## Multiple R-squared: 0.9462, Adjusted R-squared: 0.9277
## F-statistic: 50.96 on 543 and 1572 DF, p-value: < 2.2e-16Removing subzone
L3 <- lm(ResalePrice ~ .-subzone,
data = df)
summary(L3)##
## Call:
## lm(formula = ResalePrice ~ . - subzone, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -108099 -10797 0 11327 83503
##
## Coefficients: (31 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 57717.8 56921.9 1.014 0.310747
## Date2022-02-01 3205.0 2814.8 1.139 0.255040
## Date2022-03-01 6466.2 2705.6 2.390 0.016970 *
## Date2022-04-01 17158.8 2692.6 6.373 2.44e-10 ***
## Date2022-05-01 18814.9 2712.3 6.937 5.84e-12 ***
## Date2022-06-01 25490.1 2826.4 9.018 < 2e-16 ***
## Date2022-07-01 28758.1 2614.3 11.000 < 2e-16 ***
## Date2022-08-01 31702.8 2674.3 11.855 < 2e-16 ***
## Date2022-09-01 40950.6 2693.9 15.201 < 2e-16 ***
## Date2022-10-01 45604.4 2955.5 15.430 < 2e-16 ***
## Date2022-11-01 52303.1 2884.9 18.130 < 2e-16 ***
## Date2022-12-01 53873.6 2829.7 19.039 < 2e-16 ***
## Type4 ROOM 44773.9 18376.4 2.436 0.014941 *
## Type5 ROOM 109528.5 32417.7 3.379 0.000746 ***
## Block104 38496.4 28571.1 1.347 0.178050
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## Block106 12158.8 21354.2 0.569 0.569176
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## Block108 22050.0 23269.1 0.948 0.343474
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## Block113 9837.5 28592.5 0.344 0.730847
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## Block153 41538.5 21584.6 1.924 0.054478 .
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## Block156 40167.4 22615.3 1.776 0.075908 .
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## Block162A 87940.9 19513.4 4.507 7.07e-06 ***
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## Block185C 39713.5 23522.7 1.688 0.091550 .
## Block185D 40387.3 22196.8 1.820 0.069024 .
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## Block186D 1727.3 29451.9 0.059 0.953238
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## Block188B -5514.7 20500.3 -0.269 0.787961
## Block188C -47426.3 23695.6 -2.001 0.045512 *
## Block188D -33069.0 20599.9 -1.605 0.108629
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## Block192A 45345.8 23652.7 1.917 0.055400 .
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## Block193 -2958.7 20758.4 -0.143 0.886680
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## Block445B 78130.0 18992.9 4.114 4.10e-05 ***
## Block446B 69581.7 20336.3 3.422 0.000639 ***
## Block446C 44235.6 29152.6 1.517 0.129372
## Block447A 80160.3 20937.5 3.829 0.000134 ***
## Block448A 75105.9 20117.7 3.733 0.000196 ***
## Block448B 93346.2 24339.9 3.835 0.000130 ***
## Block450A 61424.4 21202.4 2.897 0.003819 **
## Block450B 100362.5 22328.7 4.495 7.47e-06 ***
## Block451A 63258.2 20698.6 3.056 0.002280 **
## Block451B 72644.6 20579.2 3.530 0.000428 ***
## Block452A 79294.6 20580.5 3.853 0.000121 ***
## Block452B 83249.5 22365.6 3.722 0.000204 ***
## Block453A 78322.1 22368.5 3.501 0.000476 ***
## Block453B 81136.6 19819.0 4.094 4.46e-05 ***
## Block453C 76924.2 20669.9 3.722 0.000205 ***
## Block453D 92619.5 20667.1 4.481 7.95e-06 ***
## Block467A 79423.8 19308.9 4.113 4.10e-05 ***
## Block467B 75099.4 18584.0 4.041 5.58e-05 ***
## Block468A 74231.5 19371.2 3.832 0.000132 ***
## Block468B 90046.0 22038.9 4.086 4.61e-05 ***
## Block468C 82243.0 19146.4 4.295 1.85e-05 ***
## Block469A 74711.4 29110.0 2.567 0.010364 *
## Block469B 88704.0 20321.3 4.365 1.35e-05 ***
## Block469C 73856.1 19307.1 3.825 0.000136 ***
## Block470A 71882.5 18557.6 3.873 0.000112 ***
## Block470B 79763.1 19899.7 4.008 6.40e-05 ***
## Block470C 68586.4 19105.7 3.590 0.000341 ***
## Block471A 83722.1 20403.2 4.103 4.28e-05 ***
## Block471B 80070.9 21020.6 3.809 0.000145 ***
## Block471C 87988.8 20985.2 4.193 2.91e-05 ***
## Block472A 111147.5 20322.5 5.469 5.25e-08 ***
## Block472B 89902.6 20407.9 4.405 1.13e-05 ***
## Block472C 100145.3 19101.1 5.243 1.80e-07 ***
## Block473A 93908.1 29718.0 3.160 0.001608 **
## years_used NA NA NA NA
## StreetANCHORVALE DR NA NA NA NA
## StreetANCHORVALE LANE NA NA NA NA
## StreetANCHORVALE LINK NA NA NA NA
## StreetANCHORVALE RD NA NA NA NA
## StreetANCHORVALE ST NA NA NA NA
## StreetCOMPASSVALE BOW NA NA NA NA
## StreetCOMPASSVALE CRES NA NA NA NA
## StreetCOMPASSVALE DR NA NA NA NA
## StreetCOMPASSVALE LANE NA NA NA NA
## StreetCOMPASSVALE LINK NA NA NA NA
## StreetCOMPASSVALE RD NA NA NA NA
## StreetCOMPASSVALE ST NA NA NA NA
## StreetCOMPASSVALE WALK NA NA NA NA
## StreetFERNVALE LANE NA NA NA NA
## StreetFERNVALE LINK NA NA NA NA
## StreetFERNVALE RD NA NA NA NA
## StreetFERNVALE ST NA NA NA NA
## StreetJLN KAYU NA NA NA NA
## StreetRIVERVALE CRES NA NA NA NA
## StreetRIVERVALE DR NA NA NA NA
## StreetRIVERVALE ST NA NA NA NA
## StreetRIVERVALE WALK NA NA NA NA
## StreetSENGKANG CTRL NA NA NA NA
## StreetSENGKANG EAST AVE NA NA NA NA
## StreetSENGKANG EAST RD NA NA NA NA
## StreetSENGKANG EAST WAY NA NA NA NA
## StreetSENGKANG WEST AVE NA NA NA NA
## StreetSENGKANG WEST WAY NA NA NA NA
## Story04 TO 06 26312.9 2131.9 12.342 < 2e-16 ***
## Story07 TO 09 46673.6 2085.4 22.381 < 2e-16 ***
## Story10 TO 12 51697.7 2153.0 24.012 < 2e-16 ***
## Story13 TO 15 59526.1 2077.3 28.656 < 2e-16 ***
## Story16 TO 18 72345.8 2615.8 27.658 < 2e-16 ***
## Story19 TO 21 67441.6 3790.2 17.794 < 2e-16 ***
## Story22 TO 24 76668.2 4256.8 18.011 < 2e-16 ***
## Story25 TO 27 77270.0 5886.0 13.128 < 2e-16 ***
## Area 2717.3 716.2 3.794 0.000154 ***
## ModelModel A 13380.1 3093.3 4.326 1.62e-05 ***
## ModelModel A2 NA NA NA NA
## ModelPremium Apartment NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23180 on 1572 degrees of freedom
## Multiple R-squared: 0.9462, Adjusted R-squared: 0.9277
## F-statistic: 50.96 on 543 and 1572 DF, p-value: < 2.2e-16It would seem removing Block would be the best. Now we will compare between street and subzone ## Removing Block and Street
L4 <- lm(ResalePrice ~ .-Block-Street,
data = df)
summary(L4)##
## Call:
## lm(formula = ResalePrice ~ . - Block - Street, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -111775 -25162 -3721 20006 172169
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 260974.1 21120.5 12.356 < 2e-16 ***
## Date2022-02-01 2414.2 4180.3 0.578 0.563656
## Date2022-03-01 3931.7 4019.8 0.978 0.328142
## Date2022-04-01 18956.2 3953.6 4.795 1.74e-06 ***
## Date2022-05-01 20446.6 4010.1 5.099 3.73e-07 ***
## Date2022-06-01 29936.2 4125.4 7.257 5.57e-13 ***
## Date2022-07-01 34120.7 3860.0 8.840 < 2e-16 ***
## Date2022-08-01 33073.6 3938.9 8.397 < 2e-16 ***
## Date2022-09-01 48602.3 3952.8 12.296 < 2e-16 ***
## Date2022-10-01 50222.4 4265.1 11.775 < 2e-16 ***
## Date2022-11-01 53405.2 4213.7 12.674 < 2e-16 ***
## Date2022-12-01 61225.8 4116.4 14.874 < 2e-16 ***
## Type4 ROOM 68329.9 8322.1 8.211 3.81e-16 ***
## Type5 ROOM 125283.1 14327.1 8.744 < 2e-16 ***
## years_used -6846.1 145.7 -46.988 < 2e-16 ***
## subzoneCompassvale 33202.2 2458.4 13.506 < 2e-16 ***
## subzoneFernvale -11416.8 2956.0 -3.862 0.000116 ***
## subzoneRivervale -14757.9 2996.5 -4.925 9.10e-07 ***
## Story04 TO 06 22522.7 3088.3 7.293 4.28e-13 ***
## Story07 TO 09 40386.8 3056.0 13.215 < 2e-16 ***
## Story10 TO 12 49134.0 3157.5 15.561 < 2e-16 ***
## Story13 TO 15 53211.7 3049.4 17.450 < 2e-16 ***
## Story16 TO 18 66251.2 3809.6 17.391 < 2e-16 ***
## Story19 TO 21 62711.0 5686.6 11.028 < 2e-16 ***
## Story22 TO 24 67144.0 6397.2 10.496 < 2e-16 ***
## Story25 TO 27 60884.6 8888.7 6.850 9.71e-12 ***
## Area 2151.6 306.2 7.026 2.86e-12 ***
## ModelModel A -6370.3 3842.6 -1.658 0.097504 .
## ModelModel A2 26486.9 6857.3 3.863 0.000116 ***
## ModelPremium Apartment 15687.1 3055.2 5.135 3.09e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 39150 on 2086 degrees of freedom
## Multiple R-squared: 0.7965, Adjusted R-squared: 0.7937
## F-statistic: 281.5 on 29 and 2086 DF, p-value: < 2.2e-16Removing Block and subzone
L5 <- lm(ResalePrice ~ .-Block-subzone, data = df)
summary(L5)##
## Call:
## lm(formula = ResalePrice ~ . - Block - subzone, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -124088 -18948 -270 17004 129236
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 206911.59 23135.45 8.943 < 2e-16 ***
## Date2022-02-01 3338.51 3170.47 1.053 0.292463
## Date2022-03-01 10296.40 3053.29 3.372 0.000759 ***
## Date2022-04-01 19656.14 2999.37 6.553 7.08e-11 ***
## Date2022-05-01 23350.74 3061.68 7.627 3.65e-14 ***
## Date2022-06-01 30759.13 3143.44 9.785 < 2e-16 ***
## Date2022-07-01 34567.35 2938.94 11.762 < 2e-16 ***
## Date2022-08-01 35800.25 3000.31 11.932 < 2e-16 ***
## Date2022-09-01 47473.78 3006.79 15.789 < 2e-16 ***
## Date2022-10-01 54249.69 3242.88 16.729 < 2e-16 ***
## Date2022-11-01 56095.57 3216.83 17.438 < 2e-16 ***
## Date2022-12-01 64365.55 3126.62 20.586 < 2e-16 ***
## Type4 ROOM 48466.79 8660.07 5.597 2.48e-08 ***
## Type5 ROOM 109702.71 15113.66 7.259 5.52e-13 ***
## years_used -7945.05 172.76 -45.988 < 2e-16 ***
## StreetANCHORVALE DR 31976.16 6270.38 5.100 3.72e-07 ***
## StreetANCHORVALE LANE -12063.89 7816.20 -1.543 0.122876
## StreetANCHORVALE LINK 12337.10 4447.85 2.774 0.005592 **
## StreetANCHORVALE RD 38.32 4704.42 0.008 0.993501
## StreetANCHORVALE ST 4975.65 5598.57 0.889 0.374249
## StreetCOMPASSVALE BOW 91750.90 5010.71 18.311 < 2e-16 ***
## StreetCOMPASSVALE CRES 6066.40 3343.44 1.814 0.069759 .
## StreetCOMPASSVALE DR 73433.80 4299.40 17.080 < 2e-16 ***
## StreetCOMPASSVALE LANE 10721.81 4382.79 2.446 0.014514 *
## StreetCOMPASSVALE LINK 107434.40 5062.84 21.220 < 2e-16 ***
## StreetCOMPASSVALE RD 47502.05 5846.44 8.125 7.63e-16 ***
## StreetCOMPASSVALE ST 7914.06 5367.01 1.475 0.140480
## StreetCOMPASSVALE WALK 44132.34 6462.40 6.829 1.12e-11 ***
## StreetFERNVALE LANE -7399.87 7597.29 -0.974 0.330164
## StreetFERNVALE LINK -10920.43 3551.25 -3.075 0.002132 **
## StreetFERNVALE RD 926.48 3979.00 0.233 0.815907
## StreetFERNVALE ST -12788.23 5996.82 -2.133 0.033083 *
## StreetJLN KAYU -12961.66 9887.74 -1.311 0.190044
## StreetRIVERVALE CRES -23855.90 3758.86 -6.347 2.70e-10 ***
## StreetRIVERVALE DR 12172.96 4859.65 2.505 0.012325 *
## StreetRIVERVALE ST 14518.22 7423.24 1.956 0.050626 .
## StreetRIVERVALE WALK 38977.29 7549.68 5.163 2.67e-07 ***
## StreetSENGKANG CTRL 112045.28 6428.06 17.431 < 2e-16 ***
## StreetSENGKANG EAST AVE 108228.75 5585.73 19.376 < 2e-16 ***
## StreetSENGKANG EAST RD 43523.78 10653.54 4.085 4.57e-05 ***
## StreetSENGKANG EAST WAY 47340.98 5326.87 8.887 < 2e-16 ***
## StreetSENGKANG WEST AVE 12712.42 9163.55 1.387 0.165506
## StreetSENGKANG WEST WAY -18907.44 4733.58 -3.994 6.72e-05 ***
## Story04 TO 06 25756.39 2346.87 10.975 < 2e-16 ***
## Story07 TO 09 43052.59 2319.59 18.560 < 2e-16 ***
## Story10 TO 12 49553.02 2396.53 20.677 < 2e-16 ***
## Story13 TO 15 57931.02 2320.00 24.970 < 2e-16 ***
## Story16 TO 18 65106.00 2888.96 22.536 < 2e-16 ***
## Story19 TO 21 62530.96 4317.69 14.483 < 2e-16 ***
## Story22 TO 24 70527.74 4870.19 14.482 < 2e-16 ***
## Story25 TO 27 64705.25 6746.42 9.591 < 2e-16 ***
## Area 2799.77 331.66 8.442 < 2e-16 ***
## ModelModel A 10520.28 3008.99 3.496 0.000482 ***
## ModelModel A2 53641.43 5443.87 9.854 < 2e-16 ***
## ModelPremium Apartment 20304.85 2637.57 7.698 2.12e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29550 on 2061 degrees of freedom
## Multiple R-squared: 0.8854, Adjusted R-squared: 0.8824
## F-statistic: 295 on 54 and 2061 DF, p-value: < 2.2e-16Comparing BIC
BIC_location <- data.frame(lm = c(".-Block",".-Street",".-subzone",".-Block-Street",".-Block-subzone"),
BIC = c(BIC(L1),BIC(L2),BIC(L3),BIC(L4),BIC(L5)))
BIC_location## lm BIC
## 1 .-Block 49895.90
## 2 .-Street 52085.02
## 3 .-subzone 52085.02
## 4 .-Block-Street 50966.23
## 5 .-Block-subzone 49941.80Checking for multicolinearity
We will notice that L4 and L5 have no perfect collinearity in the model. However, under L1, there was only one perfect collinearity found. Using our best model so far, L1, we need to fix the perfect multicolinearity present. We notice from above that L1 in fact, has perfect collinearity between Street and subzone. We will wrangle the data such that we can ommit one street while assign a binary variable to them. We will drop two of the street to ensure we do not have perfect collinerity. It is important to choose streets with a high p-value so as to see the effects of the more significant streets.
df_1 <- df %>%
tidyr::pivot_wider(names_from = Street,
values_from = Street,
values_fn = list(Street = ~1),
values_fill = 0) # Run L1 again with new df
L1_modified <- lm(ResalePrice ~.-Block,
data = df_1)
summary(L1_modified)##
## Call:
## lm(formula = ResalePrice ~ . - Block, data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -125204 -18457 -399 16719 127481
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 211856.8 25911.3 8.176 5.06e-16 ***
## Date2022-02-01 3068.5 3128.1 0.981 0.326734
## Date2022-03-01 9563.9 3012.9 3.174 0.001524 **
## Date2022-04-01 19615.9 2962.6 6.621 4.53e-11 ***
## Date2022-05-01 22646.1 3023.1 7.491 1.01e-13 ***
## Date2022-06-01 30192.6 3101.9 9.734 < 2e-16 ***
## Date2022-07-01 34028.7 2899.6 11.736 < 2e-16 ***
## Date2022-08-01 35919.8 2959.7 12.136 < 2e-16 ***
## Date2022-09-01 46772.6 2968.8 15.755 < 2e-16 ***
## Date2022-10-01 54202.7 3199.5 16.941 < 2e-16 ***
## Date2022-11-01 56565.2 3173.4 17.825 < 2e-16 ***
## Date2022-12-01 63959.6 3084.6 20.735 < 2e-16 ***
## Type4 ROOM 49571.8 8543.0 5.803 7.54e-09 ***
## Type5 ROOM 111733.1 14909.8 7.494 9.87e-14 ***
## years_used -7932.1 170.6 -46.489 < 2e-16 ***
## subzoneCompassvale 41763.7 9000.7 4.640 3.70e-06 ***
## subzoneFernvale -8749.9 14952.0 -0.585 0.558481
## subzoneRivervale -34279.2 8747.5 -3.919 9.19e-05 ***
## Story04 TO 06 25598.3 2314.9 11.058 < 2e-16 ***
## Story07 TO 09 42935.1 2288.0 18.765 < 2e-16 ***
## Story10 TO 12 48920.3 2365.7 20.679 < 2e-16 ***
## Story13 TO 15 57766.2 2289.7 25.229 < 2e-16 ***
## Story16 TO 18 66007.9 2853.4 23.133 < 2e-16 ***
## Story19 TO 21 62466.9 4258.6 14.668 < 2e-16 ***
## Story22 TO 24 70520.1 4803.4 14.681 < 2e-16 ***
## Story25 TO 27 64791.9 6653.9 9.737 < 2e-16 ***
## Area 2752.7 327.2 8.413 < 2e-16 ***
## ModelModel A 10459.1 2969.3 3.522 0.000437 ***
## ModelModel A2 52568.6 5375.9 9.778 < 2e-16 ***
## ModelPremium Apartment 20248.1 2601.8 7.782 1.12e-14 ***
## `ANCHORVALE ST` 3690.3 14269.1 0.259 0.795950
## `COMPASSVALE LANE` -32307.9 10389.7 -3.110 0.001899 **
## `FERNVALE LINK` -3616.5 7369.5 -0.491 0.623667
## `FERNVALE RD` 8271.6 7101.2 1.165 0.244229
## `FERNVALE ST` -5469.5 8778.4 -0.623 0.533308
## `RIVERVALE CRES` 8970.1 14117.2 0.635 0.525238
## `ANCHORVALE CRES` -1181.8 13779.1 -0.086 0.931662
## `COMPASSVALE CRES` -36954.9 10317.3 -3.582 0.000349 ***
## `SENGKANG EAST AVE` 65325.1 11258.2 5.802 7.55e-09 ***
## `SENGKANG WEST AVE` 19881.0 10963.2 1.813 0.069912 .
## `SENGKANG WEST WAY` -11630.2 7950.2 -1.463 0.143651
## `COMPASSVALE DR` 30334.9 10558.3 2.873 0.004106 **
## `JLN KAYU` -5462.2 11594.4 -0.471 0.637613
## `ANCHORVALE LINK` 11024.2 13676.5 0.806 0.420297
## `COMPASSVALE BOW` 48523.8 10809.3 4.489 7.55e-06 ***
## `COMPASSVALE ST` -35391.4 10556.1 -3.353 0.000815 ***
## `COMPASSVALE WALK` 1192.0 11133.6 0.107 0.914749
## `RIVERVALE ST` 47689.7 15313.6 3.114 0.001870 **
## `RIVERVALE WALK` 72099.4 15355.6 4.695 2.84e-06 ***
## `SENGKANG EAST WAY` 44927.8 12102.8 3.712 0.000211 ***
## `ANCHORVALE DR` 30545.9 14202.6 2.151 0.031614 *
## `RIVERVALE DR` 44987.6 14189.8 3.170 0.001545 **
## `ANCHORVALE RD` -1544.5 13786.7 -0.112 0.910811
## `COMPASSVALE LINK` 64066.2 10649.2 6.016 2.11e-09 ***
## `FERNVALE LANE` NA NA NA NA
## `SENGKANG CTRL` 68978.8 11459.8 6.019 2.07e-09 ***
## `COMPASSVALE RD` 4338.4 10741.2 0.404 0.686327
## `ANCHORVALE LANE` -13628.4 14990.0 -0.909 0.363369
## `SENGKANG EAST RD` NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29150 on 2058 degrees of freedom
## Multiple R-squared: 0.8887, Adjusted R-squared: 0.8857
## F-statistic: 293.4 on 56 and 2058 DF, p-value: < 2.2e-16# It is understood that Street and Subzone will be correlated. We will remove two variables from Street and rerun# We will choose ANCHORVALE LANE and FERNVALE RD that have a corresponding p-value of
L6 <- lm(ResalePrice ~.-Block-`ANCHORVALE LANE`-`FERNVALE RD`,
data = df_1)
summary(L6)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD`,
## data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -125204 -18457 -399 16719 127481
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 198228.4 23649.5 8.382 < 2e-16 ***
## Date2022-02-01 3068.5 3128.1 0.981 0.326734
## Date2022-03-01 9563.9 3012.9 3.174 0.001524 **
## Date2022-04-01 19615.9 2962.6 6.621 4.53e-11 ***
## Date2022-05-01 22646.1 3023.1 7.491 1.01e-13 ***
## Date2022-06-01 30192.6 3101.9 9.734 < 2e-16 ***
## Date2022-07-01 34028.7 2899.6 11.736 < 2e-16 ***
## Date2022-08-01 35919.8 2959.7 12.136 < 2e-16 ***
## Date2022-09-01 46772.6 2968.8 15.755 < 2e-16 ***
## Date2022-10-01 54202.7 3199.5 16.941 < 2e-16 ***
## Date2022-11-01 56565.2 3173.4 17.825 < 2e-16 ***
## Date2022-12-01 63959.6 3084.6 20.735 < 2e-16 ***
## Type4 ROOM 49571.8 8543.0 5.803 7.54e-09 ***
## Type5 ROOM 111733.1 14909.8 7.494 9.87e-14 ***
## years_used -7932.1 170.6 -46.489 < 2e-16 ***
## subzoneCompassvale 41763.7 9000.7 4.640 3.70e-06 ***
## subzoneFernvale 13150.2 7369.0 1.785 0.074486 .
## subzoneRivervale -34279.2 8747.5 -3.919 9.19e-05 ***
## Story04 TO 06 25598.3 2314.9 11.058 < 2e-16 ***
## Story07 TO 09 42935.1 2288.0 18.765 < 2e-16 ***
## Story10 TO 12 48920.3 2365.7 20.679 < 2e-16 ***
## Story13 TO 15 57766.2 2289.7 25.229 < 2e-16 ***
## Story16 TO 18 66007.9 2853.4 23.133 < 2e-16 ***
## Story19 TO 21 62466.9 4258.6 14.668 < 2e-16 ***
## Story22 TO 24 70520.1 4803.4 14.681 < 2e-16 ***
## Story25 TO 27 64791.9 6653.9 9.737 < 2e-16 ***
## Area 2752.7 327.2 8.413 < 2e-16 ***
## ModelModel A 10459.1 2969.3 3.522 0.000437 ***
## ModelModel A2 52568.6 5375.9 9.778 < 2e-16 ***
## ModelPremium Apartment 20248.1 2601.8 7.782 1.12e-14 ***
## `ANCHORVALE ST` 17318.8 8696.0 1.992 0.046550 *
## `COMPASSVALE LANE` -18679.5 11877.3 -1.573 0.115942
## `FERNVALE LINK` -11888.1 3403.0 -3.493 0.000487 ***
## `FERNVALE ST` -13741.1 5829.4 -2.357 0.018505 *
## `RIVERVALE CRES` 22598.5 11459.7 1.972 0.048744 *
## `ANCHORVALE CRES` 12446.7 7710.3 1.614 0.106617
## `COMPASSVALE CRES` -23326.4 11649.6 -2.002 0.045380 *
## `SENGKANG EAST AVE` 78953.6 12406.7 6.364 2.42e-10 ***
## `SENGKANG WEST AVE` 11609.4 8879.7 1.307 0.191220
## `SENGKANG WEST WAY` -19901.8 4576.0 -4.349 1.43e-05 ***
## `COMPASSVALE DR` 43963.3 11841.9 3.713 0.000211 ***
## `JLN KAYU` -13733.8 9620.7 -1.428 0.153580
## `ANCHORVALE LINK` 24652.6 7609.3 3.240 0.001215 **
## `COMPASSVALE BOW` 62152.2 12198.7 5.095 3.81e-07 ***
## `COMPASSVALE ST` -21763.0 11874.2 -1.833 0.066978 .
## `COMPASSVALE WALK` 14820.4 12467.0 1.189 0.234666
## `RIVERVALE ST` 61318.2 12850.4 4.772 1.96e-06 ***
## `RIVERVALE WALK` 85727.8 12906.3 6.642 3.94e-11 ***
## `SENGKANG EAST WAY` 58556.3 8901.6 6.578 6.02e-11 ***
## `ANCHORVALE DR` 44174.3 8582.0 5.147 2.89e-07 ***
## `RIVERVALE DR` 58616.0 11537.6 5.080 4.11e-07 ***
## `ANCHORVALE RD` 12083.9 7518.9 1.607 0.108178
## `COMPASSVALE LINK` 77694.6 11889.6 6.535 8.01e-11 ***
## `FERNVALE LANE` -8271.6 7101.2 -1.165 0.244229
## `SENGKANG CTRL` 82607.2 12611.3 6.550 7.23e-11 ***
## `COMPASSVALE RD` 17966.8 12186.3 1.474 0.140543
## `SENGKANG EAST RD` 13628.4 14990.0 0.909 0.363369
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29150 on 2058 degrees of freedom
## Multiple R-squared: 0.8887, Adjusted R-squared: 0.8857
## F-statistic: 293.4 on 56 and 2058 DF, p-value: < 2.2e-16BIC(L6)## [1] 49873.17We notice that after removing the 2 variables BIC lowers to 49873.17, lower than initially calculated. We also see that adjusted R square maintains at 0.8857.
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodev <- vif(L6)
v## GVIF Df GVIF^(1/(2*Df))
## Date 1.302178 11 1.012074
## Type 76.773410 2 2.960075
## years_used 3.605298 1 1.898762
## subzone 14287.238357 3 4.925966
## Story 1.603685 8 1.029959
## Area 48.537346 1 6.966875
## Model 9.598688 3 1.457814
## `ANCHORVALE ST` 3.321897 1 1.822607
## `COMPASSVALE LANE` 15.067342 1 3.881667
## `FERNVALE LINK` 2.730191 1 1.652329
## `FERNVALE ST` 1.299454 1 1.139936
## `RIVERVALE CRES` 25.842308 1 5.083533
## `ANCHORVALE CRES` 8.107005 1 2.847280
## `COMPASSVALE CRES` 35.704792 1 5.975349
## `SENGKANG EAST AVE` 6.936304 1 2.633686
## `SENGKANG WEST AVE` 1.107502 1 1.052379
## `SENGKANG WEST WAY` 1.552948 1 1.246173
## `COMPASSVALE DR` 13.619144 1 3.690412
## `JLN KAYU` 1.084400 1 1.041345
## `ANCHORVALE LINK` 5.873349 1 2.423499
## `COMPASSVALE BOW` 8.718329 1 2.952682
## `COMPASSVALE ST` 9.676052 1 3.110635
## `COMPASSVALE WALK` 9.974519 1 3.158246
## `RIVERVALE ST` 5.559951 1 2.357955
## `RIVERVALE WALK` 5.798992 1 2.408110
## `SENGKANG EAST WAY` 5.788975 1 2.406029
## `ANCHORVALE DR` 2.984216 1 1.727488
## `RIVERVALE DR` 17.179966 1 4.144872
## `ANCHORVALE RD` 5.061038 1 2.249675
## `COMPASSVALE LINK` 10.639994 1 3.261900
## `FERNVALE LANE` 1.175986 1 1.084429
## `SENGKANG CTRL` 5.354950 1 2.314076
## `COMPASSVALE RD` 7.866644 1 2.804754
## `SENGKANG EAST RD` 2.370449 1 1.539626Generally, GVIF above 2 or 3 to suggest potential multi-collinearity. Given that Street and subzone is correlated in some ways due to roads intersections with the subzones, we will bound to see some collinearity there. However, both categories are still useful for its own interpretation. For example, subzone indicates neighbourhoods clustering. There could be other variables such as proximity of schools, clinics and other facilities that attribute to the popularity of the subzone. As for streets, it could be that some streets have more buses operating or that some streets leads to expressway, contributing to ease of commute. hence, even though there are some VIF scores of 5, they are still within acceptable basis.
Visualize L6
plot(L6)
Note: We will be using L1 as the main regression and adding on to that regression. We know that the model is linear as checked under residual plots assumptions.
tmap_mode("view")## tmap mode set to interactive viewingtm_shape(sengkang_sp) +
tm_dots(col = "Area")For visualisation purposes, we plotted the Area. We notice that there is clustering of large area flats within one particular sub district. We can create an interactive term between Area and subzone.
L7 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone,
data = df_1)
summary(L7)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone, data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -125977 -18061 -289 16396 124563
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 204273.9 27855.9 7.333 3.22e-13 ***
## Date2022-02-01 3042.7 3096.6 0.983 0.325923
## Date2022-03-01 9210.3 2983.3 3.087 0.002047 **
## Date2022-04-01 19000.8 2934.7 6.475 1.19e-10 ***
## Date2022-05-01 21937.2 2994.5 7.326 3.39e-13 ***
## Date2022-06-01 29310.4 3077.3 9.525 < 2e-16 ***
## Date2022-07-01 33893.8 2874.7 11.791 < 2e-16 ***
## Date2022-08-01 36487.0 2931.3 12.447 < 2e-16 ***
## Date2022-09-01 46667.2 2939.9 15.874 < 2e-16 ***
## Date2022-10-01 53800.5 3168.1 16.982 < 2e-16 ***
## Date2022-11-01 56026.9 3142.9 17.827 < 2e-16 ***
## Date2022-12-01 63992.3 3055.8 20.941 < 2e-16 ***
## Type4 ROOM 55239.6 8690.0 6.357 2.53e-10 ***
## Type5 ROOM 117645.9 15009.3 7.838 7.28e-15 ***
## years_used -7923.4 169.7 -46.689 < 2e-16 ***
## subzoneCompassvale 14277.6 18266.1 0.782 0.434512
## subzoneFernvale 33991.8 17842.1 1.905 0.056901 .
## subzoneRivervale 52884.5 20815.0 2.541 0.011137 *
## Story04 TO 06 25872.9 2293.0 11.283 < 2e-16 ***
## Story07 TO 09 42763.9 2265.2 18.879 < 2e-16 ***
## Story10 TO 12 49393.1 2342.8 21.083 < 2e-16 ***
## Story13 TO 15 57932.5 2268.2 25.542 < 2e-16 ***
## Story16 TO 18 66590.9 2826.4 23.561 < 2e-16 ***
## Story19 TO 21 62389.3 4235.1 14.731 < 2e-16 ***
## Story22 TO 24 70534.8 4754.9 14.834 < 2e-16 ***
## Story25 TO 27 65111.8 6587.9 9.883 < 2e-16 ***
## Area 2652.7 361.9 7.330 3.30e-13 ***
## ModelModel A 4902.8 3069.7 1.597 0.110378
## ModelModel A2 43160.5 5518.0 7.822 8.26e-15 ***
## ModelPremium Apartment 18540.2 2588.4 7.163 1.10e-12 ***
## `ANCHORVALE ST` 19157.0 8634.8 2.219 0.026624 *
## `COMPASSVALE LANE` -12564.0 11810.8 -1.064 0.287556
## `FERNVALE LINK` -11095.2 3372.6 -3.290 0.001019 **
## `FERNVALE ST` -12749.5 5791.3 -2.202 0.027811 *
## `RIVERVALE CRES` 17316.0 11386.2 1.521 0.128467
## `ANCHORVALE CRES` 13826.8 7667.6 1.803 0.071493 .
## `COMPASSVALE CRES` -20526.0 11539.8 -1.779 0.075434 .
## `SENGKANG EAST AVE` 82276.7 12292.2 6.693 2.80e-11 ***
## `SENGKANG WEST AVE` 12352.7 8799.4 1.404 0.160525
## `SENGKANG WEST WAY` -19241.7 4534.1 -4.244 2.30e-05 ***
## `COMPASSVALE DR` 46908.9 11732.1 3.998 6.60e-05 ***
## `JLN KAYU` -12592.7 9526.5 -1.322 0.186365
## `ANCHORVALE LINK` 26486.7 7546.1 3.510 0.000458 ***
## `COMPASSVALE BOW` 65764.5 12089.2 5.440 5.97e-08 ***
## `COMPASSVALE ST` -20992.5 11754.9 -1.786 0.074271 .
## `COMPASSVALE WALK` 15736.7 12344.3 1.275 0.202517
## `RIVERVALE ST` 67939.5 12764.4 5.323 1.13e-07 ***
## `RIVERVALE WALK` 93255.6 12831.9 7.267 5.18e-13 ***
## `SENGKANG EAST WAY` 59481.7 8814.6 6.748 1.94e-11 ***
## `ANCHORVALE DR` 44328.0 8498.1 5.216 2.01e-07 ***
## `RIVERVALE DR` 60519.7 11426.4 5.296 1.31e-07 ***
## `ANCHORVALE RD` 12009.2 7443.1 1.613 0.106795
## `COMPASSVALE LINK` 80880.9 11783.9 6.864 8.85e-12 ***
## `FERNVALE LANE` -9426.8 7033.2 -1.340 0.180287
## `SENGKANG CTRL` 86053.1 12501.3 6.884 7.73e-12 ***
## `COMPASSVALE RD` 18718.9 12064.1 1.552 0.120908
## `SENGKANG EAST RD` 17259.4 14851.6 1.162 0.245320
## subzoneCompassvale:Area 252.7 155.1 1.630 0.103319
## subzoneFernvale:Area -203.1 163.8 -1.240 0.215144
## subzoneRivervale:Area -832.4 182.8 -4.555 5.55e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28850 on 2055 degrees of freedom
## Multiple R-squared: 0.8911, Adjusted R-squared: 0.888
## F-statistic: 285 on 59 and 2055 DF, p-value: < 2.2e-16BIC(L7)## [1] 49850.05We notice that adjusted R square went up and BIC went down to 49850 as compared to 49873.17. We notice that subzone are no longer significant except for rivervale. We can say that the interaction between Area and subzone is condensed in Rivervale and that contributes to the Resale price. We know that area is also affected by the number of rooms under type. We will add Type into the interaction as well.
L8 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type,
data = df_1)
summary(L8)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone * Type, data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -121050 -16012 -783 15722 124041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 201726.3 67872.8 2.972 0.002992 **
## Date2022-02-01 2933.9 3024.5 0.970 0.332137
## Date2022-03-01 9030.3 2921.3 3.091 0.002021 **
## Date2022-04-01 18580.7 2872.6 6.468 1.24e-10 ***
## Date2022-05-01 21617.5 2929.5 7.379 2.30e-13 ***
## Date2022-06-01 27876.9 3012.9 9.253 < 2e-16 ***
## Date2022-07-01 33426.3 2806.8 11.909 < 2e-16 ***
## Date2022-08-01 36511.7 2862.2 12.757 < 2e-16 ***
## Date2022-09-01 45744.8 2867.3 15.954 < 2e-16 ***
## Date2022-10-01 52972.0 3091.6 17.134 < 2e-16 ***
## Date2022-11-01 55415.7 3065.8 18.076 < 2e-16 ***
## Date2022-12-01 63696.4 2987.8 21.319 < 2e-16 ***
## Type4 ROOM 274443.1 144208.6 1.903 0.057168 .
## Type5 ROOM -1439284.4 240576.7 -5.983 2.59e-09 ***
## years_used -7733.8 172.0 -44.951 < 2e-16 ***
## subzoneCompassvale -690537.7 694378.7 -0.994 0.320113
## subzoneFernvale -359649.6 303141.4 -1.186 0.235599
## subzoneRivervale 404541.5 1011075.6 0.400 0.689117
## Story04 TO 06 25629.5 2236.8 11.458 < 2e-16 ***
## Story07 TO 09 42330.2 2210.3 19.151 < 2e-16 ***
## Story10 TO 12 49159.9 2287.4 21.492 < 2e-16 ***
## Story13 TO 15 58066.9 2215.7 26.207 < 2e-16 ***
## Story16 TO 18 66267.0 2758.7 24.021 < 2e-16 ***
## Story19 TO 21 64825.2 4157.2 15.594 < 2e-16 ***
## Story22 TO 24 71094.7 4647.9 15.296 < 2e-16 ***
## Story25 TO 27 64999.1 6431.0 10.107 < 2e-16 ***
## Area 2757.1 948.4 2.907 0.003688 **
## ModelModel A 5869.4 3069.1 1.912 0.055961 .
## ModelModel A2 32272.9 6141.3 5.255 1.63e-07 ***
## ModelPremium Apartment 20664.1 2574.6 8.026 1.68e-15 ***
## `ANCHORVALE ST` 20932.8 8492.9 2.465 0.013793 *
## `COMPASSVALE LANE` 7247.8 12039.3 0.602 0.547233
## `FERNVALE LINK` -5687.1 3452.1 -1.647 0.099620 .
## `FERNVALE ST` -7426.9 5787.4 -1.283 0.199536
## `RIVERVALE CRES` 25980.5 11430.6 2.273 0.023136 *
## `ANCHORVALE CRES` 14455.8 7596.8 1.903 0.057195 .
## `COMPASSVALE CRES` -4195.3 11633.0 -0.361 0.718410
## `SENGKANG EAST AVE` 98262.7 12341.7 7.962 2.79e-15 ***
## `SENGKANG WEST AVE` 11918.1 8701.6 1.370 0.170951
## `SENGKANG WEST WAY` -10134.6 4838.3 -2.095 0.036322 *
## `COMPASSVALE DR` 62430.7 11760.1 5.309 1.22e-07 ***
## `JLN KAYU` -6323.7 9337.3 -0.677 0.498327
## `ANCHORVALE LINK` 34667.2 7537.2 4.599 4.50e-06 ***
## `COMPASSVALE BOW` 79783.8 12174.1 6.554 7.09e-11 ***
## `COMPASSVALE ST` -7342.6 11702.9 -0.627 0.530458
## `COMPASSVALE WALK` 47510.1 13037.0 3.644 0.000275 ***
## `RIVERVALE ST` 72494.2 13445.7 5.392 7.79e-08 ***
## `RIVERVALE WALK` 96714.2 13661.8 7.079 1.99e-12 ***
## `SENGKANG EAST WAY` 69556.3 8810.0 7.895 4.69e-15 ***
## `ANCHORVALE DR` 59855.9 8703.7 6.877 8.09e-12 ***
## `RIVERVALE DR` 67900.3 11462.6 5.924 3.69e-09 ***
## `ANCHORVALE RD` 20303.6 7335.3 2.768 0.005693 **
## `COMPASSVALE LINK` 87894.1 11806.8 7.444 1.43e-13 ***
## `FERNVALE LANE` -5720.4 6951.1 -0.823 0.410631
## `SENGKANG CTRL` 97427.9 12523.2 7.780 1.14e-14 ***
## `COMPASSVALE RD` 30827.3 11935.9 2.583 0.009871 **
## `SENGKANG EAST RD` 24835.6 14641.8 1.696 0.089999 .
## subzoneCompassvale:Area 10191.1 10243.6 0.995 0.319912
## subzoneFernvale:Area 5475.7 4453.1 1.230 0.218971
## subzoneRivervale:Area -6444.4 15020.1 -0.429 0.667929
## Type4 ROOM:Area -2563.1 1697.3 -1.510 0.131186
## Type5 ROOM:Area 13854.6 2315.6 5.983 2.58e-09 ***
## Type4 ROOM:subzoneCompassvale 740624.5 707494.0 1.047 0.295303
## Type5 ROOM:subzoneCompassvale 2425708.5 735130.9 3.300 0.000985 ***
## Type4 ROOM:subzoneFernvale -438453.5 347325.1 -1.262 0.206959
## Type5 ROOM:subzoneFernvale 1630054.0 455450.3 3.579 0.000353 ***
## Type4 ROOM:subzoneRivervale -564324.5 1019144.7 -0.554 0.579829
## Type5 ROOM:subzoneRivervale 1124902.3 1040440.2 1.081 0.279745
## Type4 ROOM:subzoneCompassvale:Area -10393.9 10353.0 -1.004 0.315522
## Type5 ROOM:subzoneCompassvale:Area -25493.0 10481.7 -2.432 0.015095 *
## Type4 ROOM:subzoneFernvale:Area 3277.5 4792.9 0.684 0.494170
## Type5 ROOM:subzoneFernvale:Area -16815.2 5380.6 -3.125 0.001802 **
## Type4 ROOM:subzoneRivervale:Area 7959.0 15088.2 0.528 0.597902
## Type5 ROOM:subzoneRivervale:Area -7730.8 15191.2 -0.509 0.610878
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28090 on 2041 degrees of freedom
## Multiple R-squared: 0.8975, Adjusted R-squared: 0.8938
## F-statistic: 244.7 on 73 and 2041 DF, p-value: < 2.2e-16BIC(L8)## [1] 49829.95We will want to include another interaction variable here. This time with Model. Model indicates the current condition of the house as well. Base on the research done, Model A and A2 are older generation models, Premium has a similar structure to Model A and A2 but comes with newer amenities, Improved are units that went through upgrading works. We will interact Model with the years_used.
L9 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used,
data = df_1)
summary(L9)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone * Type + Model * years_used, data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -118353 -16184 -1043 15695 119172
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 245281.7 65576.9 3.740 0.000189 ***
## Date2022-02-01 2394.9 2917.3 0.821 0.411776
## Date2022-03-01 9391.9 2821.7 3.328 0.000889 ***
## Date2022-04-01 18053.0 2772.9 6.511 9.40e-11 ***
## Date2022-05-01 23021.6 2831.0 8.132 7.25e-16 ***
## Date2022-06-01 28804.4 2906.2 9.911 < 2e-16 ***
## Date2022-07-01 33304.4 2707.6 12.300 < 2e-16 ***
## Date2022-08-01 36381.7 2762.2 13.171 < 2e-16 ***
## Date2022-09-01 46212.6 2769.1 16.689 < 2e-16 ***
## Date2022-10-01 53990.9 2982.5 18.102 < 2e-16 ***
## Date2022-11-01 56670.3 2957.4 19.162 < 2e-16 ***
## Date2022-12-01 62995.0 2881.1 21.865 < 2e-16 ***
## Type4 ROOM 83233.3 141821.6 0.587 0.557344
## Type5 ROOM -671659.3 241994.2 -2.776 0.005562 **
## years_used -9209.5 259.3 -35.511 < 2e-16 ***
## subzoneCompassvale -771233.7 669598.3 -1.152 0.249544
## subzoneFernvale -267509.2 292326.6 -0.915 0.360245
## subzoneRivervale 134314.6 974950.1 0.138 0.890439
## Story04 TO 06 25257.5 2157.1 11.709 < 2e-16 ***
## Story07 TO 09 42614.0 2135.3 19.957 < 2e-16 ***
## Story10 TO 12 49925.6 2206.4 22.627 < 2e-16 ***
## Story13 TO 15 58014.0 2136.3 27.156 < 2e-16 ***
## Story16 TO 18 65888.8 2660.9 24.762 < 2e-16 ***
## Story19 TO 21 65345.5 4008.2 16.303 < 2e-16 ***
## Story22 TO 24 70850.3 4481.1 15.811 < 2e-16 ***
## Story25 TO 27 65073.7 6199.8 10.496 < 2e-16 ***
## Area 2510.5 914.7 2.745 0.006109 **
## ModelModel A -40099.9 5049.9 -7.941 3.29e-15 ***
## ModelModel A2 -72339.8 60839.8 -1.189 0.234570
## ModelPremium Apartment 9967.3 5364.0 1.858 0.063284 .
## `ANCHORVALE ST` 14575.8 8256.4 1.765 0.077647 .
## `COMPASSVALE LANE` -3329.8 11702.6 -0.285 0.776026
## `FERNVALE LINK` -1946.7 3350.2 -0.581 0.561269
## `FERNVALE ST` -6213.7 5586.3 -1.112 0.266138
## `RIVERVALE CRES` 13593.4 11082.0 1.227 0.220109
## `ANCHORVALE CRES` 7399.0 7473.0 0.990 0.322244
## `COMPASSVALE CRES` -24176.1 11466.4 -2.108 0.035116 *
## `SENGKANG EAST AVE` 78623.1 12135.6 6.479 1.16e-10 ***
## `SENGKANG WEST AVE` 8217.2 8395.6 0.979 0.327821
## `SENGKANG WEST WAY` -10711.8 4665.8 -2.296 0.021788 *
## `COMPASSVALE DR` 43365.4 11616.0 3.733 0.000194 ***
## `JLN KAYU` -8205.6 9002.7 -0.911 0.362165
## `ANCHORVALE LINK` 26020.1 7384.0 3.524 0.000435 ***
## `COMPASSVALE BOW` 68171.4 11783.7 5.785 8.36e-09 ***
## `COMPASSVALE ST` -17662.3 11330.4 -1.559 0.119189
## `COMPASSVALE WALK` 28033.3 12850.7 2.181 0.029264 *
## `RIVERVALE ST` 47835.6 13277.2 3.603 0.000322 ***
## `RIVERVALE WALK` 71016.9 13528.3 5.250 1.68e-07 ***
## `SENGKANG EAST WAY` 57057.0 8760.3 6.513 9.25e-11 ***
## `ANCHORVALE DR` 49833.7 8661.0 5.754 1.00e-08 ***
## `RIVERVALE DR` 49599.5 11283.4 4.396 1.16e-05 ***
## `ANCHORVALE RD` 11597.1 7208.4 1.609 0.107809
## `COMPASSVALE LINK` 76107.8 11437.2 6.654 3.64e-11 ***
## `FERNVALE LANE` -2076.6 6754.5 -0.307 0.758542
## `SENGKANG CTRL` 85004.7 12144.7 6.999 3.48e-12 ***
## `COMPASSVALE RD` 20138.1 11703.0 1.721 0.085446 .
## `SENGKANG EAST RD` 2441.2 14343.7 0.170 0.864874
## subzoneCompassvale:Area 11514.2 9878.1 1.166 0.243900
## subzoneFernvale:Area 4146.3 4294.2 0.966 0.334373
## subzoneRivervale:Area -2169.4 14483.9 -0.150 0.880951
## Type4 ROOM:Area -347.3 1666.3 -0.208 0.834923
## Type5 ROOM:Area 7075.1 2315.6 3.055 0.002276 **
## Type4 ROOM:subzoneCompassvale 1067016.7 682906.2 1.562 0.118334
## Type5 ROOM:subzoneCompassvale 1665016.7 711517.8 2.340 0.019375 *
## Type4 ROOM:subzoneFernvale -213984.0 336280.7 -0.636 0.524636
## Type5 ROOM:subzoneFernvale 650272.8 447108.7 1.454 0.145991
## Type4 ROOM:subzoneRivervale -68586.7 983529.5 -0.070 0.944411
## Type5 ROOM:subzoneRivervale 495092.3 1004994.9 0.493 0.622326
## years_used:ModelModel A 3484.0 292.7 11.903 < 2e-16 ***
## years_used:ModelModel A2 5419.1 2789.7 1.943 0.052207 .
## years_used:ModelPremium Apartment 516.3 342.5 1.508 0.131819
## Type4 ROOM:subzoneCompassvale:Area -14371.0 9989.2 -1.439 0.150402
## Type5 ROOM:subzoneCompassvale:Area -19168.9 10117.6 -1.895 0.058284 .
## Type4 ROOM:subzoneFernvale:Area 1125.6 4632.2 0.243 0.808031
## Type5 ROOM:subzoneFernvale:Area -7666.3 5245.7 -1.461 0.144050
## Type4 ROOM:subzoneRivervale:Area 1224.5 14557.6 0.084 0.932976
## Type5 ROOM:subzoneRivervale:Area -3786.0 14653.0 -0.258 0.796142
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27080 on 2038 degrees of freedom
## Multiple R-squared: 0.9048, Adjusted R-squared: 0.9013
## F-statistic: 255 on 76 and 2038 DF, p-value: < 2.2e-16BIC(L9)## [1] 49694.8Generally, I would like to know whether higher floors tend to have higher prices.
L10 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2),
data = df_1)
summary(L10)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone * Type + Model * years_used + I(Area^2), data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -118136 -16436 -1070 15593 118433
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1639149.46 405856.27 4.039 5.57e-05 ***
## Date2022-02-01 2552.64 2909.75 0.877 0.380443
## Date2022-03-01 9703.18 2815.49 3.446 0.000580 ***
## Date2022-04-01 17941.67 2765.56 6.488 1.09e-10 ***
## Date2022-05-01 23277.17 2824.25 8.242 3.00e-16 ***
## Date2022-06-01 28871.82 2898.42 9.961 < 2e-16 ***
## Date2022-07-01 33243.16 2700.32 12.311 < 2e-16 ***
## Date2022-08-01 36514.12 2754.98 13.254 < 2e-16 ***
## Date2022-09-01 46260.79 2761.64 16.751 < 2e-16 ***
## Date2022-10-01 54137.47 2974.72 18.199 < 2e-16 ***
## Date2022-11-01 57043.75 2951.36 19.328 < 2e-16 ***
## Date2022-12-01 63219.73 2874.00 21.997 < 2e-16 ***
## Type4 ROOM 854842.23 263003.64 3.250 0.001172 **
## Type5 ROOM 1091014.45 561089.81 1.944 0.051978 .
## years_used -9545.26 276.05 -34.578 < 2e-16 ***
## subzoneCompassvale -981975.20 670521.14 -1.464 0.143213
## subzoneFernvale -525977.23 300846.07 -1.748 0.080558 .
## subzoneRivervale -88803.07 974415.38 -0.091 0.927395
## Story04 TO 06 25505.50 2152.47 11.849 < 2e-16 ***
## Story07 TO 09 42737.63 2129.75 20.067 < 2e-16 ***
## Story10 TO 12 50085.71 2200.93 22.757 < 2e-16 ***
## Story13 TO 15 58418.23 2133.66 27.379 < 2e-16 ***
## Story16 TO 18 66376.12 2657.35 24.978 < 2e-16 ***
## Story19 TO 21 65420.22 3997.41 16.366 < 2e-16 ***
## Story22 TO 24 71070.57 4469.41 15.902 < 2e-16 ***
## Story25 TO 27 65491.44 6184.09 10.590 < 2e-16 ***
## Area -34697.85 10731.32 -3.233 0.001243 **
## ModelModel A -39812.45 5036.84 -7.904 4.38e-15 ***
## ModelModel A2 -149274.99 64577.18 -2.312 0.020900 *
## ModelPremium Apartment 8576.08 5364.32 1.599 0.110036
## `ANCHORVALE ST` 13651.48 8238.26 1.657 0.097657 .
## `COMPASSVALE LANE` -2111.25 11676.06 -0.181 0.856528
## `FERNVALE LINK` -2823.59 3350.64 -0.843 0.399495
## `FERNVALE ST` -6932.60 5574.98 -1.244 0.213819
## `RIVERVALE CRES` 14743.64 11056.87 1.333 0.182538
## `ANCHORVALE CRES` 5944.91 7464.43 0.796 0.425874
## `COMPASSVALE CRES` -22872.78 11441.39 -1.999 0.045727 *
## `SENGKANG EAST AVE` 79115.85 12103.48 6.537 7.93e-11 ***
## `SENGKANG WEST AVE` 9170.49 8377.28 1.095 0.273783
## `SENGKANG WEST WAY` -11190.02 4655.19 -2.404 0.016316 *
## `COMPASSVALE DR` 43803.20 11585.15 3.781 0.000161 ***
## `JLN KAYU` -7837.35 8978.92 -0.873 0.382842
## `ANCHORVALE LINK` 25773.28 7364.31 3.500 0.000476 ***
## `COMPASSVALE BOW` 68926.23 11753.68 5.864 5.25e-09 ***
## `COMPASSVALE ST` -15064.32 11324.25 -1.330 0.183578
## `COMPASSVALE WALK` 27134.07 12818.45 2.117 0.034398 *
## `RIVERVALE ST` 49632.43 13251.20 3.746 0.000185 ***
## `RIVERVALE WALK` 69563.02 13498.03 5.154 2.80e-07 ***
## `SENGKANG EAST WAY` 58682.80 8749.03 6.707 2.56e-11 ***
## `ANCHORVALE DR` 51167.60 8645.98 5.918 3.81e-09 ***
## `RIVERVALE DR` 54279.10 11332.82 4.790 1.79e-06 ***
## `ANCHORVALE RD` 11385.84 7189.11 1.584 0.113403
## `COMPASSVALE LINK` 74844.31 11411.95 6.558 6.87e-11 ***
## `FERNVALE LANE` -683.04 6748.01 -0.101 0.919385
## `SENGKANG CTRL` 85719.19 12113.48 7.076 2.03e-12 ***
## `COMPASSVALE RD` 22916.26 11698.50 1.959 0.050260 .
## `SENGKANG EAST RD` 3960.27 14311.39 0.277 0.782022
## I(Area^2) 245.71 70.61 3.480 0.000512 ***
## subzoneCompassvale:Area 14631.15 9891.87 1.479 0.139266
## subzoneFernvale:Area 7987.42 4422.49 1.806 0.071052 .
## subzoneRivervale:Area 1117.05 14475.40 0.077 0.938497
## Type4 ROOM:Area -9245.26 3049.53 -3.032 0.002462 **
## Type5 ROOM:Area -11390.93 5787.25 -1.968 0.049171 *
## Type4 ROOM:subzoneCompassvale 1309674.79 684613.02 1.913 0.055886 .
## Type5 ROOM:subzoneCompassvale 1996740.57 715960.91 2.789 0.005338 **
## Type4 ROOM:subzoneFernvale 17284.62 341889.50 0.051 0.959684
## Type5 ROOM:subzoneFernvale 859177.64 449918.05 1.910 0.056321 .
## Type4 ROOM:subzoneRivervale 204833.76 984001.77 0.208 0.835122
## Type5 ROOM:subzoneRivervale 810247.73 1006350.30 0.805 0.420836
## years_used:ModelModel A 3443.57 292.15 11.787 < 2e-16 ***
## years_used:ModelModel A2 8458.97 2916.02 2.901 0.003761 **
## years_used:ModelPremium Apartment 691.36 345.25 2.002 0.045365 *
## Type4 ROOM:subzoneCompassvale:Area -17851.93 10012.15 -1.783 0.074731 .
## Type5 ROOM:subzoneCompassvale:Area -23378.48 10162.35 -2.300 0.021521 *
## Type4 ROOM:subzoneFernvale:Area -2425.48 4730.96 -0.513 0.608228
## Type5 ROOM:subzoneFernvale:Area -11069.70 5322.12 -2.080 0.037656 *
## Type4 ROOM:subzoneRivervale:Area -2630.18 14560.30 -0.181 0.856667
## Type5 ROOM:subzoneRivervale:Area -7915.74 14661.36 -0.540 0.589322
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27010 on 2037 degrees of freedom
## Multiple R-squared: 0.9054, Adjusted R-squared: 0.9018
## F-statistic: 253.2 on 77 and 2037 DF, p-value: < 2.2e-16BIC(L10)## [1] 49689.92I am alittle skeptical whether the relationship between Area and Resale Price, years_used and Resale price is linear due to the plots above.
We will test the regression between Resale Price and this variable alone to see whether higher terms would result in a better result
BIC for L10 decreased while Adjusted Rsquare went up, suggesting that this is a better model.
L11 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2),
data = df_1)
summary(L11)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone * Type + Model * years_used + I(Area^2), data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -118136 -16436 -1070 15593 118433
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1639149.46 405856.27 4.039 5.57e-05 ***
## Date2022-02-01 2552.64 2909.75 0.877 0.380443
## Date2022-03-01 9703.18 2815.49 3.446 0.000580 ***
## Date2022-04-01 17941.67 2765.56 6.488 1.09e-10 ***
## Date2022-05-01 23277.17 2824.25 8.242 3.00e-16 ***
## Date2022-06-01 28871.82 2898.42 9.961 < 2e-16 ***
## Date2022-07-01 33243.16 2700.32 12.311 < 2e-16 ***
## Date2022-08-01 36514.12 2754.98 13.254 < 2e-16 ***
## Date2022-09-01 46260.79 2761.64 16.751 < 2e-16 ***
## Date2022-10-01 54137.47 2974.72 18.199 < 2e-16 ***
## Date2022-11-01 57043.75 2951.36 19.328 < 2e-16 ***
## Date2022-12-01 63219.73 2874.00 21.997 < 2e-16 ***
## Type4 ROOM 854842.23 263003.64 3.250 0.001172 **
## Type5 ROOM 1091014.45 561089.81 1.944 0.051978 .
## years_used -9545.26 276.05 -34.578 < 2e-16 ***
## subzoneCompassvale -981975.20 670521.14 -1.464 0.143213
## subzoneFernvale -525977.23 300846.07 -1.748 0.080558 .
## subzoneRivervale -88803.07 974415.38 -0.091 0.927395
## Story04 TO 06 25505.50 2152.47 11.849 < 2e-16 ***
## Story07 TO 09 42737.63 2129.75 20.067 < 2e-16 ***
## Story10 TO 12 50085.71 2200.93 22.757 < 2e-16 ***
## Story13 TO 15 58418.23 2133.66 27.379 < 2e-16 ***
## Story16 TO 18 66376.12 2657.35 24.978 < 2e-16 ***
## Story19 TO 21 65420.22 3997.41 16.366 < 2e-16 ***
## Story22 TO 24 71070.57 4469.41 15.902 < 2e-16 ***
## Story25 TO 27 65491.44 6184.09 10.590 < 2e-16 ***
## Area -34697.85 10731.32 -3.233 0.001243 **
## ModelModel A -39812.45 5036.84 -7.904 4.38e-15 ***
## ModelModel A2 -149274.99 64577.18 -2.312 0.020900 *
## ModelPremium Apartment 8576.08 5364.32 1.599 0.110036
## `ANCHORVALE ST` 13651.48 8238.26 1.657 0.097657 .
## `COMPASSVALE LANE` -2111.25 11676.06 -0.181 0.856528
## `FERNVALE LINK` -2823.59 3350.64 -0.843 0.399495
## `FERNVALE ST` -6932.60 5574.98 -1.244 0.213819
## `RIVERVALE CRES` 14743.64 11056.87 1.333 0.182538
## `ANCHORVALE CRES` 5944.91 7464.43 0.796 0.425874
## `COMPASSVALE CRES` -22872.78 11441.39 -1.999 0.045727 *
## `SENGKANG EAST AVE` 79115.85 12103.48 6.537 7.93e-11 ***
## `SENGKANG WEST AVE` 9170.49 8377.28 1.095 0.273783
## `SENGKANG WEST WAY` -11190.02 4655.19 -2.404 0.016316 *
## `COMPASSVALE DR` 43803.20 11585.15 3.781 0.000161 ***
## `JLN KAYU` -7837.35 8978.92 -0.873 0.382842
## `ANCHORVALE LINK` 25773.28 7364.31 3.500 0.000476 ***
## `COMPASSVALE BOW` 68926.23 11753.68 5.864 5.25e-09 ***
## `COMPASSVALE ST` -15064.32 11324.25 -1.330 0.183578
## `COMPASSVALE WALK` 27134.07 12818.45 2.117 0.034398 *
## `RIVERVALE ST` 49632.43 13251.20 3.746 0.000185 ***
## `RIVERVALE WALK` 69563.02 13498.03 5.154 2.80e-07 ***
## `SENGKANG EAST WAY` 58682.80 8749.03 6.707 2.56e-11 ***
## `ANCHORVALE DR` 51167.60 8645.98 5.918 3.81e-09 ***
## `RIVERVALE DR` 54279.10 11332.82 4.790 1.79e-06 ***
## `ANCHORVALE RD` 11385.84 7189.11 1.584 0.113403
## `COMPASSVALE LINK` 74844.31 11411.95 6.558 6.87e-11 ***
## `FERNVALE LANE` -683.04 6748.01 -0.101 0.919385
## `SENGKANG CTRL` 85719.19 12113.48 7.076 2.03e-12 ***
## `COMPASSVALE RD` 22916.26 11698.50 1.959 0.050260 .
## `SENGKANG EAST RD` 3960.27 14311.39 0.277 0.782022
## I(Area^2) 245.71 70.61 3.480 0.000512 ***
## subzoneCompassvale:Area 14631.15 9891.87 1.479 0.139266
## subzoneFernvale:Area 7987.42 4422.49 1.806 0.071052 .
## subzoneRivervale:Area 1117.05 14475.40 0.077 0.938497
## Type4 ROOM:Area -9245.26 3049.53 -3.032 0.002462 **
## Type5 ROOM:Area -11390.93 5787.25 -1.968 0.049171 *
## Type4 ROOM:subzoneCompassvale 1309674.79 684613.02 1.913 0.055886 .
## Type5 ROOM:subzoneCompassvale 1996740.57 715960.91 2.789 0.005338 **
## Type4 ROOM:subzoneFernvale 17284.62 341889.50 0.051 0.959684
## Type5 ROOM:subzoneFernvale 859177.64 449918.05 1.910 0.056321 .
## Type4 ROOM:subzoneRivervale 204833.76 984001.77 0.208 0.835122
## Type5 ROOM:subzoneRivervale 810247.73 1006350.30 0.805 0.420836
## years_used:ModelModel A 3443.57 292.15 11.787 < 2e-16 ***
## years_used:ModelModel A2 8458.97 2916.02 2.901 0.003761 **
## years_used:ModelPremium Apartment 691.36 345.25 2.002 0.045365 *
## Type4 ROOM:subzoneCompassvale:Area -17851.93 10012.15 -1.783 0.074731 .
## Type5 ROOM:subzoneCompassvale:Area -23378.48 10162.35 -2.300 0.021521 *
## Type4 ROOM:subzoneFernvale:Area -2425.48 4730.96 -0.513 0.608228
## Type5 ROOM:subzoneFernvale:Area -11069.70 5322.12 -2.080 0.037656 *
## Type4 ROOM:subzoneRivervale:Area -2630.18 14560.30 -0.181 0.856667
## Type5 ROOM:subzoneRivervale:Area -7915.74 14661.36 -0.540 0.589322
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27010 on 2037 degrees of freedom
## Multiple R-squared: 0.9054, Adjusted R-squared: 0.9018
## F-statistic: 253.2 on 77 and 2037 DF, p-value: < 2.2e-16BIC(L11)## [1] 49689.92L12 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2) +I(Area^3),
data = df_1)
summary(L12)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone * Type + Model * years_used + I(Area^2) +
## I(Area^3), data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -118447 -16203 -1061 15729 118665
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.060e+06 1.648e+06 3.069 0.002174 **
## Date2022-02-01 2.396e+03 2.908e+03 0.824 0.410086
## Date2022-03-01 9.808e+03 2.813e+03 3.486 0.000500 ***
## Date2022-04-01 1.783e+04 2.764e+03 6.451 1.39e-10 ***
## Date2022-05-01 2.341e+04 2.822e+03 8.295 < 2e-16 ***
## Date2022-06-01 2.878e+04 2.896e+03 9.937 < 2e-16 ***
## Date2022-07-01 3.328e+04 2.698e+03 12.336 < 2e-16 ***
## Date2022-08-01 3.657e+04 2.753e+03 13.286 < 2e-16 ***
## Date2022-09-01 4.625e+04 2.759e+03 16.764 < 2e-16 ***
## Date2022-10-01 5.402e+04 2.973e+03 18.172 < 2e-16 ***
## Date2022-11-01 5.692e+04 2.949e+03 19.299 < 2e-16 ***
## Date2022-12-01 6.316e+04 2.872e+03 21.993 < 2e-16 ***
## Type4 ROOM 1.520e+06 4.068e+05 3.736 0.000192 ***
## Type5 ROOM 1.692e+06 6.269e+05 2.699 0.007021 **
## years_used -9.398e+03 2.842e+02 -33.067 < 2e-16 ***
## subzoneCompassvale -1.369e+06 6.939e+05 -1.973 0.048625 *
## subzoneFernvale -8.810e+05 3.433e+05 -2.566 0.010351 *
## subzoneRivervale -4.573e+05 9.887e+05 -0.463 0.643722
## Story04 TO 06 2.548e+04 2.151e+03 11.848 < 2e-16 ***
## Story07 TO 09 4.273e+04 2.128e+03 20.080 < 2e-16 ***
## Story10 TO 12 5.003e+04 2.199e+03 22.750 < 2e-16 ***
## Story13 TO 15 5.847e+04 2.132e+03 27.424 < 2e-16 ***
## Story16 TO 18 6.642e+04 2.655e+03 25.017 < 2e-16 ***
## Story19 TO 21 6.541e+04 3.994e+03 16.377 < 2e-16 ***
## Story22 TO 24 7.099e+04 4.466e+03 15.898 < 2e-16 ***
## Story25 TO 27 6.553e+04 6.179e+03 10.606 < 2e-16 ***
## Area -1.480e+05 5.401e+04 -2.741 0.006186 **
## ModelModel A -3.726e+04 5.172e+03 -7.204 8.19e-13 ***
## ModelModel A2 -1.886e+05 6.708e+04 -2.811 0.004986 **
## ModelPremium Apartment 9.621e+03 5.382e+03 1.788 0.073974 .
## `ANCHORVALE ST` 1.423e+04 8.235e+03 1.727 0.084255 .
## `COMPASSVALE LANE` -1.913e+03 1.167e+04 -0.164 0.869791
## `FERNVALE LINK` -2.909e+03 3.348e+03 -0.869 0.385016
## `FERNVALE ST` -6.904e+03 5.570e+03 -1.239 0.215307
## `RIVERVALE CRES` 1.463e+04 1.105e+04 1.324 0.185495
## `ANCHORVALE CRES` 6.504e+03 7.462e+03 0.872 0.383567
## `COMPASSVALE CRES` -2.302e+04 1.143e+04 -2.014 0.044168 *
## `SENGKANG EAST AVE` 7.909e+04 1.209e+04 6.541 7.73e-11 ***
## `SENGKANG WEST AVE` 9.673e+03 8.373e+03 1.155 0.248147
## `SENGKANG WEST WAY` -1.116e+04 4.651e+03 -2.400 0.016473 *
## `COMPASSVALE DR` 4.366e+04 1.158e+04 3.772 0.000167 ***
## `JLN KAYU` -7.523e+03 8.972e+03 -0.838 0.401874
## `ANCHORVALE LINK` 2.642e+04 7.364e+03 3.588 0.000342 ***
## `COMPASSVALE BOW` 6.850e+04 1.175e+04 5.832 6.36e-09 ***
## `COMPASSVALE ST` -1.539e+04 1.132e+04 -1.360 0.173907
## `COMPASSVALE WALK` 2.647e+04 1.281e+04 2.066 0.038930 *
## `RIVERVALE ST` 5.063e+04 1.325e+04 3.822 0.000136 ***
## `RIVERVALE WALK` 7.016e+04 1.349e+04 5.202 2.17e-07 ***
## `SENGKANG EAST WAY` 5.951e+04 8.750e+03 6.801 1.36e-11 ***
## `ANCHORVALE DR` 5.151e+04 8.640e+03 5.961 2.94e-09 ***
## `RIVERVALE DR` 5.370e+04 1.133e+04 4.741 2.27e-06 ***
## `ANCHORVALE RD` 1.204e+04 7.189e+03 1.674 0.094270 .
## `COMPASSVALE LINK` 7.390e+04 1.141e+04 6.476 1.18e-10 ***
## `FERNVALE LANE` -7.774e+02 6.742e+03 -0.115 0.908216
## `SENGKANG CTRL` 8.519e+04 1.211e+04 7.037 2.67e-12 ***
## `COMPASSVALE RD` 2.222e+04 1.169e+04 1.900 0.057573 .
## `SENGKANG EAST RD` 4.333e+03 1.430e+04 0.303 0.761924
## I(Area^2) 1.432e+03 5.588e+02 2.563 0.010438 *
## I(Area^3) -3.847e+00 1.797e+00 -2.141 0.032409 *
## subzoneCompassvale:Area 2.041e+04 1.025e+04 1.992 0.046461 *
## subzoneFernvale:Area 1.329e+04 5.065e+03 2.624 0.008768 **
## subzoneRivervale:Area 6.618e+03 1.469e+04 0.451 0.652362
## Type4 ROOM:Area -1.697e+04 4.724e+03 -3.593 0.000334 ***
## Type5 ROOM:Area -1.865e+04 6.703e+03 -2.782 0.005446 **
## Type4 ROOM:subzoneCompassvale 1.705e+06 7.085e+05 2.406 0.016202 *
## Type5 ROOM:subzoneCompassvale 2.312e+06 7.303e+05 3.165 0.001573 **
## Type4 ROOM:subzoneFernvale 3.633e+05 3.779e+05 0.961 0.336437
## Type5 ROOM:subzoneFernvale 1.256e+06 4.862e+05 2.583 0.009861 **
## Type4 ROOM:subzoneRivervale 5.902e+05 9.995e+05 0.590 0.554939
## Type5 ROOM:subzoneRivervale 1.130e+06 1.017e+06 1.112 0.266395
## years_used:ModelModel A 3.167e+03 3.193e+02 9.918 < 2e-16 ***
## years_used:ModelModel A2 9.856e+03 2.986e+03 3.301 0.000980 ***
## years_used:ModelPremium Apartment 5.766e+02 3.491e+02 1.652 0.098761 .
## Type4 ROOM:subzoneCompassvale:Area -2.371e+04 1.037e+04 -2.286 0.022335 *
## Type5 ROOM:subzoneCompassvale:Area -2.851e+04 1.043e+04 -2.733 0.006334 **
## Type4 ROOM:subzoneFernvale:Area -7.623e+03 5.314e+03 -1.435 0.151552
## Type5 ROOM:subzoneFernvale:Area -1.674e+04 5.940e+03 -2.818 0.004884 **
## Type4 ROOM:subzoneRivervale:Area -8.306e+03 1.479e+04 -0.562 0.574377
## Type5 ROOM:subzoneRivervale:Area -1.298e+04 1.484e+04 -0.875 0.381892
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 26980 on 2036 degrees of freedom
## Multiple R-squared: 0.9056, Adjusted R-squared: 0.902
## F-statistic: 250.5 on 78 and 2036 DF, p-value: < 2.2e-16BIC(L12)## [1] 49692.83plot(df_1$Area, residuals(L11))
We can use higher term for Area Moving on to years_used
L13 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2) + I(years_used^2),
data = df_1)
summary(L13)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone * Type + Model * years_used + I(Area^2) +
## I(years_used^2), data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -119977 -16328 -987 15539 118966
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1494752.80 406696.22 3.675 0.000244 ***
## Date2022-02-01 2479.51 2901.44 0.855 0.392885
## Date2022-03-01 9720.65 2807.38 3.463 0.000546 ***
## Date2022-04-01 18092.56 2757.91 6.560 6.79e-11 ***
## Date2022-05-01 23570.34 2817.31 8.366 < 2e-16 ***
## Date2022-06-01 28647.10 2890.75 9.910 < 2e-16 ***
## Date2022-07-01 33183.62 2692.59 12.324 < 2e-16 ***
## Date2022-08-01 36675.89 2747.42 13.349 < 2e-16 ***
## Date2022-09-01 46012.38 2754.56 16.704 < 2e-16 ***
## Date2022-10-01 53987.86 2966.44 18.200 < 2e-16 ***
## Date2022-11-01 56462.59 2947.34 19.157 < 2e-16 ***
## Date2022-12-01 63315.41 2865.84 22.093 < 2e-16 ***
## Type4 ROOM 797851.80 262729.62 3.037 0.002422 **
## Type5 ROOM 917360.67 561576.49 1.634 0.102509
## years_used -14059.52 1291.98 -10.882 < 2e-16 ***
## subzoneCompassvale -839746.62 669771.05 -1.254 0.210065
## subzoneFernvale -463241.79 300491.76 -1.542 0.123323
## subzoneRivervale 240399.84 975958.92 0.246 0.805458
## Story04 TO 06 25841.38 2148.32 12.029 < 2e-16 ***
## Story07 TO 09 43112.81 2126.21 20.277 < 2e-16 ***
## Story10 TO 12 50312.69 2195.51 22.916 < 2e-16 ***
## Story13 TO 15 58747.85 2129.50 27.588 < 2e-16 ***
## Story16 TO 18 66593.05 2650.39 25.126 < 2e-16 ***
## Story19 TO 21 65286.61 3986.07 16.379 < 2e-16 ***
## Story22 TO 24 71510.54 4458.23 16.040 < 2e-16 ***
## Story25 TO 27 66480.28 6172.47 10.770 < 2e-16 ***
## Area -30429.26 10766.77 -2.826 0.004756 **
## ModelModel A -40875.10 5031.11 -8.124 7.71e-16 ***
## ModelModel A2 -112009.83 65228.83 -1.717 0.086098 .
## ModelPremium Apartment 9241.35 5352.09 1.727 0.084377 .
## `ANCHORVALE ST` 18116.00 8308.85 2.180 0.029347 *
## `COMPASSVALE LANE` 11316.44 12232.91 0.925 0.355033
## `FERNVALE LINK` -7743.35 3613.14 -2.143 0.032223 *
## `FERNVALE ST` -11188.02 5684.85 -1.968 0.049199 *
## `RIVERVALE CRES` 24452.77 11354.38 2.154 0.031389 *
## `ANCHORVALE CRES` 5618.23 7443.48 0.755 0.450465
## `COMPASSVALE CRES` -17498.20 11506.99 -1.521 0.128501
## `SENGKANG EAST AVE` 87707.82 12305.42 7.128 1.41e-12 ***
## `SENGKANG WEST AVE` 12238.13 8397.07 1.457 0.145153
## `SENGKANG WEST WAY` -12855.36 4665.08 -2.756 0.005910 **
## `COMPASSVALE DR` 49251.83 11651.81 4.227 2.47e-05 ***
## `JLN KAYU` -6632.87 8959.38 -0.740 0.459187
## `ANCHORVALE LINK` 28856.06 7393.52 3.903 9.81e-05 ***
## `COMPASSVALE BOW` 77549.05 11965.28 6.481 1.14e-10 ***
## `COMPASSVALE ST` -9978.65 11380.82 -0.877 0.380701
## `COMPASSVALE WALK` 32754.40 12877.78 2.543 0.011049 *
## `RIVERVALE ST` 55585.49 13317.47 4.174 3.12e-05 ***
## `RIVERVALE WALK` 74808.56 13538.83 5.525 3.71e-08 ***
## `SENGKANG EAST WAY` 62587.04 8791.87 7.119 1.50e-12 ***
## `ANCHORVALE DR` 53024.01 8636.69 6.139 9.93e-10 ***
## `RIVERVALE DR` 59854.76 11407.21 5.247 1.71e-07 ***
## `ANCHORVALE RD` 13282.50 7187.99 1.848 0.064765 .
## `COMPASSVALE LINK` 87620.64 11926.73 7.347 2.93e-13 ***
## `FERNVALE LANE` -3383.72 6770.82 -0.500 0.617305
## `SENGKANG CTRL` 99654.29 12691.56 7.852 6.57e-15 ***
## `COMPASSVALE RD` 27690.40 11740.94 2.358 0.018446 *
## `SENGKANG EAST RD` 8069.47 14316.34 0.564 0.573051
## I(Area^2) 219.09 70.80 3.095 0.001998 **
## I(years_used^2) 167.25 46.77 3.576 0.000357 ***
## subzoneCompassvale:Area 12397.76 9883.12 1.254 0.209827
## subzoneFernvale:Area 7121.35 4416.40 1.612 0.107012
## subzoneRivervale:Area -3906.09 14501.88 -0.269 0.787687
## Type4 ROOM:Area -8661.86 3045.12 -2.845 0.004492 **
## Type5 ROOM:Area -9663.71 5790.75 -1.669 0.095307 .
## Type4 ROOM:subzoneCompassvale 1194465.96 683400.23 1.748 0.080645 .
## Type5 ROOM:subzoneCompassvale 1909271.31 714316.92 2.673 0.007581 **
## Type4 ROOM:subzoneFernvale -53653.26 341481.05 -0.157 0.875166
## Type5 ROOM:subzoneFernvale 819039.64 448762.10 1.825 0.068131 .
## Type4 ROOM:subzoneRivervale -106008.49 985009.16 -0.108 0.914306
## Type5 ROOM:subzoneRivervale 514383.23 1006855.50 0.511 0.609490
## years_used:ModelModel A 3527.19 292.24 12.069 < 2e-16 ***
## years_used:ModelModel A2 6611.76 2953.14 2.239 0.025271 *
## years_used:ModelPremium Apartment 787.80 345.31 2.281 0.022628 *
## Type4 ROOM:subzoneCompassvale:Area -15970.82 9997.15 -1.598 0.110301
## Type5 ROOM:subzoneCompassvale:Area -21685.21 10144.13 -2.138 0.032659 *
## Type4 ROOM:subzoneFernvale:Area -1396.48 4726.09 -0.295 0.767655
## Type5 ROOM:subzoneFernvale:Area -10344.39 5310.66 -1.948 0.051570 .
## Type4 ROOM:subzoneRivervale:Area 2117.43 14578.92 0.145 0.884536
## Type5 ROOM:subzoneRivervale:Area -3256.45 14677.06 -0.222 0.824435
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 26930 on 2036 degrees of freedom
## Multiple R-squared: 0.906, Adjusted R-squared: 0.9024
## F-statistic: 251.6 on 78 and 2036 DF, p-value: < 2.2e-16BIC(L13)## [1] 49684.34L14 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2) + I(years_used^2) + I(years_used^3),
data = df_1)
summary(L14)##
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` +
## Area * subzone * Type + Model * years_used + I(Area^2) +
## I(years_used^2) + I(years_used^3), data = df_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -118280 -16373 -839 15409 118408
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.528e+06 4.067e+05 3.758 0.000176 ***
## Date2022-02-01 2.646e+03 2.900e+03 0.913 0.361584
## Date2022-03-01 9.845e+03 2.806e+03 3.509 0.000460 ***
## Date2022-04-01 1.832e+04 2.758e+03 6.643 3.93e-11 ***
## Date2022-05-01 2.377e+04 2.816e+03 8.439 < 2e-16 ***
## Date2022-06-01 2.900e+04 2.893e+03 10.024 < 2e-16 ***
## Date2022-07-01 3.372e+04 2.702e+03 12.479 < 2e-16 ***
## Date2022-08-01 3.727e+04 2.759e+03 13.506 < 2e-16 ***
## Date2022-09-01 4.676e+04 2.775e+03 16.851 < 2e-16 ***
## Date2022-10-01 5.489e+04 2.995e+03 18.330 < 2e-16 ***
## Date2022-11-01 5.750e+04 2.986e+03 19.259 < 2e-16 ***
## Date2022-12-01 6.432e+04 2.902e+03 22.161 < 2e-16 ***
## Type4 ROOM 7.254e+05 2.647e+05 2.740 0.006196 **
## Type5 ROOM 8.318e+05 5.626e+05 1.479 0.139386
## years_used -2.065e+04 3.376e+03 -6.117 1.14e-09 ***
## subzoneCompassvale -8.777e+05 6.694e+05 -1.311 0.189989
## subzoneFernvale -4.399e+05 3.004e+05 -1.464 0.143308
## subzoneRivervale 3.508e+05 9.765e+05 0.359 0.719435
## Story04 TO 06 2.591e+04 2.147e+03 12.070 < 2e-16 ***
## Story07 TO 09 4.317e+04 2.125e+03 20.319 < 2e-16 ***
## Story10 TO 12 5.031e+04 2.194e+03 22.936 < 2e-16 ***
## Story13 TO 15 5.862e+04 2.129e+03 27.537 < 2e-16 ***
## Story16 TO 18 6.667e+04 2.648e+03 25.174 < 2e-16 ***
## Story19 TO 21 6.524e+04 3.983e+03 16.382 < 2e-16 ***
## Story22 TO 24 7.156e+04 4.454e+03 16.064 < 2e-16 ***
## Story25 TO 27 6.686e+04 6.170e+03 10.836 < 2e-16 ***
## Area -3.038e+04 1.076e+04 -2.824 0.004794 **
## ModelModel A -4.106e+04 5.028e+03 -8.167 5.49e-16 ***
## ModelModel A2 -1.388e+05 6.639e+04 -2.091 0.036689 *
## ModelPremium Apartment 1.154e+04 5.457e+03 2.115 0.034576 *
## `ANCHORVALE ST` 1.772e+04 8.304e+03 2.133 0.033014 *
## `COMPASSVALE LANE` 6.024e+03 1.248e+04 0.483 0.629242
## `FERNVALE LINK` -8.086e+03 3.614e+03 -2.237 0.025362 *
## `FERNVALE ST` -1.091e+04 5.682e+03 -1.920 0.055024 .
## `RIVERVALE CRES` 1.638e+04 1.197e+04 1.369 0.171291
## `ANCHORVALE CRES` 2.854e+03 7.551e+03 0.378 0.705516
## `COMPASSVALE CRES` -2.433e+04 1.194e+04 -2.037 0.041747 *
## `SENGKANG EAST AVE` 8.349e+04 1.246e+04 6.703 2.63e-11 ***
## `SENGKANG WEST AVE` 1.233e+04 8.390e+03 1.469 0.141963
## `SENGKANG WEST WAY` -1.226e+04 4.669e+03 -2.626 0.008692 **
## `COMPASSVALE DR` 4.308e+04 1.200e+04 3.589 0.000340 ***
## `JLN KAYU` -5.830e+03 8.960e+03 -0.651 0.515296
## `ANCHORVALE LINK` 2.773e+04 7.406e+03 3.745 0.000186 ***
## `COMPASSVALE BOW` 7.109e+04 1.234e+04 5.761 9.65e-09 ***
## `COMPASSVALE ST` -1.426e+04 1.155e+04 -1.234 0.217180
## `COMPASSVALE WALK` 2.915e+04 1.298e+04 2.246 0.024826 *
## `RIVERVALE ST` 4.974e+04 1.359e+04 3.660 0.000259 ***
## `RIVERVALE WALK` 7.016e+04 1.370e+04 5.119 3.35e-07 ***
## `SENGKANG EAST WAY` 5.859e+04 8.986e+03 6.520 8.81e-11 ***
## `ANCHORVALE DR` 5.059e+04 8.706e+03 5.811 7.17e-09 ***
## `RIVERVALE DR` 5.381e+04 1.175e+04 4.579 4.95e-06 ***
## `ANCHORVALE RD` 1.234e+04 7.196e+03 1.714 0.086593 .
## `COMPASSVALE LINK` 8.194e+04 1.222e+04 6.708 2.55e-11 ***
## `FERNVALE LANE` -5.076e+03 6.812e+03 -0.745 0.456287
## `SENGKANG CTRL` 9.435e+04 1.293e+04 7.299 4.14e-13 ***
## `COMPASSVALE RD` 2.309e+04 1.193e+04 1.936 0.053056 .
## `SENGKANG EAST RD` 3.389e+03 1.447e+04 0.234 0.814897
## I(Area^2) 2.163e+02 7.075e+01 3.057 0.002265 **
## I(years_used^2) 7.535e+02 2.813e+02 2.679 0.007448 **
## I(years_used^3) -1.514e+01 7.162e+00 -2.114 0.034674 *
## subzoneCompassvale:Area 1.299e+04 9.879e+03 1.315 0.188648
## subzoneFernvale:Area 6.734e+03 4.416e+03 1.525 0.127504
## subzoneRivervale:Area -5.466e+03 1.451e+04 -0.377 0.706398
## Type4 ROOM:Area -7.790e+03 3.070e+03 -2.537 0.011249 *
## Type5 ROOM:Area -8.738e+03 5.802e+03 -1.506 0.132235
## Type4 ROOM:subzoneCompassvale 1.230e+06 6.830e+05 1.801 0.071847 .
## Type5 ROOM:subzoneCompassvale 1.936e+06 7.138e+05 2.713 0.006732 **
## Type4 ROOM:subzoneFernvale -7.347e+03 3.419e+05 -0.021 0.982857
## Type5 ROOM:subzoneFernvale 8.475e+05 4.486e+05 1.889 0.059001 .
## Type4 ROOM:subzoneRivervale -2.146e+05 9.855e+05 -0.218 0.827645
## Type5 ROOM:subzoneRivervale 3.905e+05 1.008e+06 0.387 0.698438
## years_used:ModelModel A 3.539e+03 2.920e+02 12.119 < 2e-16 ***
## years_used:ModelModel A2 7.995e+03 3.022e+03 2.645 0.008225 **
## years_used:ModelPremium Apartment 4.989e+02 3.711e+02 1.344 0.178943
## Type4 ROOM:subzoneCompassvale:Area -1.650e+04 9.992e+03 -1.651 0.098869 .
## Type5 ROOM:subzoneCompassvale:Area -2.215e+04 1.014e+04 -2.184 0.029045 *
## Type4 ROOM:subzoneFernvale:Area -1.773e+03 4.725e+03 -0.375 0.707586
## Type5 ROOM:subzoneFernvale:Area -1.043e+04 5.306e+03 -1.965 0.049537 *
## Type4 ROOM:subzoneRivervale:Area 3.723e+03 1.459e+04 0.255 0.798559
## Type5 ROOM:subzoneRivervale:Area -1.522e+03 1.469e+04 -0.104 0.917492
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 26910 on 2035 degrees of freedom
## Multiple R-squared: 0.9062, Adjusted R-squared: 0.9026
## F-statistic: 248.9 on 79 and 2035 DF, p-value: < 2.2e-16BIC(L14)## [1] 49687.36Based on the BIC, years_used provides a smaller BIC at higher term ^2.
library(fitdistrplus)## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## Loading required package: survivalfnorm <- fitdist(residuals(L14), "norm")## Warning in sqrt(diag(varcovar)): NaNs produced## Warning in sqrt(1/diag(V)): NaNs produced## Warning in cov2cor(varcovar): diag(.) had 0 or NA entries; non-finite result is doubtfulresult <- gofstat(fnorm, discrete = FALSE)
result## Goodness-of-fit statistics
## 1-mle-norm
## Kolmogorov-Smirnov statistic 0.03108534
## Cramer-von Mises statistic 0.72967187
## Anderson-Darling statistic 4.62404065
##
## Goodness-of-fit criteria
## 1-mle-norm
## Akaike's Information Criterion 49071.16
## Bayesian Information Criterion 49082.47KScritvalue <-1.36/sqrt(length(df$Date))
KScritvalue## [1] 0.02956522summary(fnorm)## Fitting of the distribution ' norm ' by maximum likelihood
## Parameters :
## estimate Std. Error
## mean 1.358867e-12 NaN
## sd 2.639320e+04 NaN
## Loglikelihood: -24533.58 AIC: 49071.16 BIC: 49082.47
## Correlation matrix:
## mean sd
## mean 1 NaN
## sd NaN 1plot(fnorm)
Since KS statistics = 0.032744 > 0.02956522=Kcrit, we can reject the null hypothesis and thus the data do provide sufficient evidence to show the normal model is the appropriate model.